Lengyel, Gáspár & Tarnai have looked into the question of what are the roundest polyhedra constrained to having higher order symmetries. Note that Fowler, Cremona & Steer give a method of constructing medial polyhedra having tetrahedral symmetry. Many of these are good candidates for "roundest".

Table 1-5 lists the best known polyhedra with tetrahedral, octahedral or icosahedral symmetry.

Polyhedra listed by Lengyel, Gáspár & Tarnai are listed here when they have not been superceded by one having a greater IQ. When they are the best known regardless of symmetry the data is from the Monte Carlo searches. Otherwise the polyhedra were recreated from their descriptions and Schoen's roll-toward-centroid routine was used to maximize the IQs. In all cases the IQs were found to match the Lengyel, et al. values.

Many listed here with tetrahedral symmetry and *n>43* are putative best regardless
of symmetry and were found using my recreation of Schoen's Monte Carlo search routine
(*n≤200*) or my pentagon-distance constrained medial polyhedron and heptagon
augmentaion searches (*186≤n≤504*). Of special note is *n=468* which has
12 heptagonal faces.

Fowler, Cremona & Steer extend the Goldberg-Coxeter construction to generating polyhedra other than the regular simplices. In particular they use a twisted, truncated tetrahedron as a master polyhedron with a pair of Goldberg-Coxeter parameters. The first parameter defines the main, face triangle, and one side of the edge truncation triangles. And the second parameter defines a second side of the edge triangles and the sides of the vertex (small) triangles. This construction provides a means of systematically exploring medial polyhedra having T symmetry.

*n=24*: The result of optimizing the Fowler-Cremona-Steer *(2,0,0,1)* is
the pentagonal icositetrahedron (dual of the snub cube) which Lengyel, et al. have suggested
as a candidate. This was optimized by using a single face
normal surrounded by five duplicates put into place using octahedral symmetry operations.
Fewer than 100 roll-toward-centroid iterations were needed to obtain a maximized IQ of
0.873501076. Unlike the snub cube dual the faces of the resulting polyhedron do not
exhibit bilateral symmetry. They have an apex angle of about 81.6°.
Another way to produce this polyhedron is by placing pyramidal caps on the square faces
of the octahedral Goldberg *(2,1)*.

*n=28* and *n=40*: The symmetries for these are incorrectly identified in Schoen's
1986 paper and supplement as C_{3} and C_{3v}. They are T and T_{d} respectively.
1000000 Monte Carlo trials for each found no better solutions than these two.

*n=34*: It appears that the tetrahedral Goldberg *(4,0)* cannont be constructed to
meet Lindelöf condition of coincidence of face tangents and face centroids.
Its greatest IQ is about 0.90185.
The listed polyhedron was found with a Montecarlo search by fixing the normals of six faces to the
2-fold axes, and the nomals of four faces to one pole of the 3-fold axes.

*n=36*: Generated from Fowler-Cremona-Steer *(1,2,0,2)*. This is typical of a large
class of cases. A candidate with octahedral symmetry may be created by truncating the edges
of the pentagonal icositetrahedron (*n=24*) at its 2-fold axes and optimizing
(octsym.36.3d) but the resulting IQ is only 0.906732858.

*n=44*: The case for this one is similar to that for *n=24* in that a candidate
with octahedral symmetry may be constructed by capping the
six squares of the octahedral Goldberg *(2,2)* with pyramids.
This polyhedron has three face types, two are hexagonal and one pentagonal.
One of the hexagonal types are centered on the two-fold octahedral axes, and the
other are centered on the three-fold axes. Thus only the pentagonal face normals must
be determined to maximize its IQ: 0.931040736 (octsym.44.3d).
But a polyhedron with tetrahedral symmetry may be constructed using the
Fowler-Cremona-Steer parameter *(3,0,1,1)* which has an IQ of 0.9310502002 when
optimized.

*n=50*: While tetrahedrally symmetric polyhedra seem to be good candidates, Fowler et al. show
that there are no medial polyhedra with tetrahedral symmetry with
vertex counts *4×2 ^{n}×3^{m}*.
By adding 12 pentagon-heptagon pairs we may find non-medial tetrahedrally symmetric
polyhedra for these vertex counts.

The the next larger polyhedron without a medial T symmetric polyhedron is *n=50*.
Here *a=3*. Truncating alternate vertices of the octahedral
Goldberg polyhedron *(1,1)* either once or twice and optimizing for IQ results in
the entry for *n=50* in Table 1-5 having an IQ of
0.938451113. Another candidate with octahedral symmetry is the Goldberg polyhedron
*(2,2)* (octsym.50.3d), but this has an optimized IQ of 0.938021543.

*n=56*: This is another case for which there are no medial polyhedra with T symmetry.
But two were found having 12 heptagonal faces. A compact description has not yet been
developed to describe this class of polyhedra.

*n=60*: The pentagonal hexecontahedron (dual of the snub dodecahedron) was found to have an
IQ of 0.945897296 when optimized, but Fowler-Cremona-Steer *(1,2,-1,3)* when optimized has an
IQ of 0.949386159.

*n=66*: The octahedral Goldberg *(4,0)* has an optimized IQ of 0.952728804.
While there is no medial T polyhedron for this face count there is one with 12 heptagonal
faces with an IQ of 0.952898940.

*n=86*: Fowler-Cremona-Steer *(1,4,-1,2)* degenerates to a polyhedron
with O_{h} symmetry consisting of six squares, 24 pentagons, 24 heptagons and 32
hexagons, and an IQ of 0.964386507. The heptagons have two short sides of about 0.003 when
the polyhedron is circumscribed around a unit sphere.
Another candidate is the octahedral Goldberg *(4,1)*,
which does not appear to be able to meet the Lindelöf conditions, but has an IQ of about 0.96397.

The polyhedron for *n=468* found by the general search suggested the possibile
existence of a case where a polyhedron with 12 heptagonal faces and tetrahedral symmetry
has a larger IQ than an icosahedral Goldberg polyhedron with the same number of faces.
A search found such a case for *n=492* where one was found with and IQ of 0.993826897
compared to the optimized icosahedral Goldberg polyhedra *(5,3)* at 0.993826705, and
*(7,0)* at 0.993824606.

Table 1-6 is a quick survey of other polyhedra
having tetrahedral symmetry for values of *n* not in Table 1-5. No attempt has been
made to identify planes of symmetry.

The existance of polyhedra with heptagonal faces and tetrahedral symmetry suggests the possibility of polyhedra with heptagonal faces and icosahedral symmetry. These must have a multiple of 60 heptagonal faces. For this reason the simple method of replacing each pentagonal face with a heptagon and two attendent pentagons will not work. Also, the pentagons are on the five-fold rotational axes.

The Goldberg polyhedra (15,11) and (19,6) having 5112 faces were used to attempt to generate some examples. Two face normals were deleted from each one-third face of the generating icosahedron, and this pattern was propagated using icosahedral symmetry operations. The roll-toward centroid process was then used to heal the resulting defects and maximize the IQ. Table 1-7 lists some of the resulting polyhedra that retain icosahedral symmetry and have IQs greater than Goldberg polyhedron (18,7) which has the same number of faces.

n | G | S | IQ | upper bound | normals^{ a} | polyhedron^{ b} | model^{ i} | notes |
---|---|---|---|---|---|---|---|---|

4 | (1,0) | T_{d} | 0.302299894039^{ c} | 0.302299894039 | minvol.4.txt | minvol.4.off | minvol.4.3d | Proven, Tóth |

6 | (1,0) | O_{h} | 0.523598775598^{ c} | 0.523598775598 | minvol.6.txt | minvol.6.off | minvol.6.3d | Proven, Tóth |

8 | (1,1)^{ e} | O_{h} | 0.604599788078 | 0.637349714015 | octsym.8.txt | octsym.8.off | octsym.8.3d | Proven, Lengyel, Gáspár & Tarnai |

10 | (2,0) | T_{d} | 0.630745372290 | 0.707318712042 | tetsym.10.txt | tetsym.10.off | tetsym.10.3d | Proven, Lengyel, Gáspár & Tarnai |

12 | (1,0) | I_{h} | 0.754697399337^{ c} | 0.754697399337 | minvol.12.txt | minvol.12.off | minvol.12.3d | Proven, Tóth |

14 | (1,1) | O_{h} | 0.781638893326 | 0.788894402368 | octsym.14.txt | octsym.14.off | octsym.14.3d | Proven, Lengyel, Gáspár & Tarnai |

16 | (1,1,0,1) | T_{d} | 0.812189097959^{ d} | 0.814733609959 | minvol.16.txt | minvol.16.off | minvol.16.3d | Goldberg |

18 | (2,0) | O_{h} | 0.823218074449 | 0.834942754338 | octsym.18.txt | octsym.18.off | octsym.18.3d | Lengyel, Gáspár & Tarnai |

20 | (3,0) | T_{d} | 0.830222439252 | 0.851179828648 | tetsym.20.txt | tetsym.20.off | tetsym.20.3d | Lengyel, Gáspár & Tarnai |

22 | (1,1,-1,1) | T_{d} | 0.862408738134 | 0.864510388893 | tetsym.22.txt | tetsym.22.off | tetsym.22.3d | Lengyel, Gáspár & Tarnai |

24 | (2,1)^{ f} | O | 0.873501076099 | 0.875650339164 | octsym.24.txt | octsym.24.off | octsym.24.3d | Deeter |

26 | (2,0)^{ g} | O_{h} | 0.876811430883 | 0.885098414627 | octsym.26.txt | octsym.26.off | octsym.26.3d | Huybers |

28 | (2,0,1,1) | T | 0.891896903082^{ d} | 0.893212692575 | minvol.28.txt | minvol.28.off | minvol.28.3d | Schoen (identified as C_{3}) |

30 | (2,1) | O | 0.896930384030 | 0.900256896589 | octsym.30.txt | octsym.30.off | octsym.30.3d | Lengyel, Gáspár & Tarnai |

32 | (1,1) | I_{h} | 0.905798260224^{ d} | 0.906429544276 | minvol.32.txt | minvol.32.off | minvol.32.3d | Goldberg |

34 | (?) | T | 0.904877388595 | 0.911882921464 | tetsym.34.txt | tetsym.34.off | tetsym.34.3d | Deeter |

36 | (1,2,0,2) | T_{d} | 0.915097355369 | 0.916735796857 | tetsym.36.txt | tetsym.36.off | tetsym.36.3d | Deeter |

38 | (3,0) | O_{h} | 0.917445003352 | 0.921082160244 | octsym.38.txt | octsym.38.off | octsym.38.3d | Lengyel, Gáspár & Tarnai |

40 | (2,0,-1,2) | T_{d} | 0.924263462401^{ d} | 0.924997362965 | minvol.40.txt | minvol.40.off | minvol.40.3d | Schoen (identified as C_{3v}) |

42 | (2,0) | I_{h} | 0.927651905322 | 0.928542518938 | g_2_0.txt | g_2_0.off | g_2_0.3d | Goldberg |

44 | (3,0,1,1) | T_{d} | 0.931050200233 | 0.931767715087 | tetsym.44.txt | tetsym.44.off | tetsym.44.3d | Deeter |

46 | (1,2,-1,2) | T | 0.933970892417^{ d} | 0.934714390669 | minvol.46.txt | minvol.46.off | minvol.46.3d | Deeter |

48 | (2,1,0,2) | T | 0.936791510872 | 0.937417126110 | tetsym.48.txt | tetsym.48.off | tetsym.48.3d | Deeter |

50 | (1,1)^{ j} | T_{h} | 0.938451113328 | 0.939905005491 | tetsym.50.txt | tetsym.50.off | tetsym.50.3d | Deeter |

52 | (2,1,-1,2) | T | 0.941483414618 | 0.942202666696 | tetsym.52.txt | tetsym.52.off | tetsym.52.3d | Deeter |

54 | (?) | O | 0.942664343757 | 0.944331119684 | octsym.54.txt | octsym.54.off | octsym.54.3d | Deeter |

56 | (?) | T | 0.944349081159 | 0.946308390471 | tetsym.56.txt | tetsym.56.off | tetsym.56.3d | Deeter |

58 | (2,2,0,2) | T_{d} | 0.947397931319 | 0.948150032663 | tetsym.58.txt | tetsym.58.off | tetsym.58.3d | Deeter |

60 | (1,2,-1,3) | T_{h} | 0.949386158784 | 0.949869537255 | tetsym.60.txt | tetsym.60.off | tetsym.60.3d | Deeter |

62 | (3,0,-1,2) | T_{d} | 0.950649958795 | 0.951478663539 | tetsym.62.txt | tetsym.62.off | tetsym.62.3d | Deeter |

64 | (3,0,0,2) | T | 0.952419592450 | 0.952987708298 | tetsym.64.txt | tetsym.64.off | tetsym.64.3d | Deeter |

66 | (?) | T | 0.952898940228 | 0.954405726300 | tetsym.66.txt | tetsym.66.off | tetsym.66.3d | Deeter |

68 | (2,2,-1,2) | T | 0.955005716590 | 0.955740712069 | tetsym.68.txt | tetsym.68.off | tetsym.68.3d | Deeter |

70 | (3,0,1,2) | T | 0.956582257907 | 0.956999750645 | tetsym.70.txt | tetsym.70.off | tetsym.70.3d | Deeter |

72 | (2,1) | I | 0.957881213238^{ d} | 0.958189143332 | minvol.72.txt | minvol.72.off | minvol.72.3d | Tarnai et al. |

74 | (?) | T | 0.958250244082 | 0.959314513146 | tetsym.74.txt | tetsym.74.off | tetsym.74.3d | Deeter |

76 | (3,1,2,2) | T | 0.959719648931 | 0.960380893684 | tetsym.76.txt | tetsym.76.off | tetsym.76.3d | Deeter |

78 | (2,1,-2,3) | T_{h} | 0.961091884930^{ d} | 0.961392804377 | minvol.78.txt | minvol.78.off | minvol.78.3d | Deeter |

80 | (2,2,0,3) | T | 0.961937579785 | 0.962354314504 | tetsym.80.txt | tetsym.80.off | tetsym.80.3d | Deeter |

82 | (2,2,-2,2) | T_{d} | 0.962743044099 | 0.963269097873 | tetsym.82.txt | tetsym.82.off | tetsym.82.3d | Deeter |

84 | (1,3,-2,2) | T | 0.963622531470 | 0.964140479721 | tetsym.84.txt | tetsym.84.off | tetsym.84.3d | Deeter |

86 | (1,4,-1,2)^{ k} | O_{h} | 0.964386506791 | 0.964971477096 | octsym.86.txt | octsym.86.off | octsym.86.3d | Deeter |

88 | (3,0,-1,3) | T | 0.965472924542 | 0.965764833752 | tetsym.88.txt | tetsym.88.off | tetsym.88.3d | Deeter |

90 | (4,0,0,2) | T | 0.965984144705 | 0.966523050404 | tetsym.90.txt | tetsym.90.off | tetsym.90.3d | Deeter |

92 | (3,0) | I_{h} | 0.966957236637 | 0.967248411057 | g_3_0.txt | g_3_0.off | g_3_0.3d | Lengyel, Gáspár & Tarnai |

94 | (2,3,0,3) | T_{d} | 0.967549699708 | 0.967943005983 | tetsym.94.txt | tetsym.94.off | tetsym.94.3d | Deeter |

96 | (1,3,-2,3) | T | 0.968324216310 | 0.968608751832 | tetsym.96.txt | tetsym.96.off | tetsym.96.3d | Deeter |

98 | (?) | T_{d} | 0.968537193755 | 0.969247409294 | tetsym.98.txt | tetsym.98.off | tetsym.98.3d | Deeter |

100 | (3,1,0,3) | T | 0.969609143820 | 0.969860598643 | tetsym.100.txt | tetsym.100.off | tetsym.100.3d | Deeter |

102 | (3,1,-1,3) | T | 0.970172216654 | 0.970449813463 | tetsym.102.txt | tetsym.102.off | tetsym.102.3d | Deeter |

104 | (4,1,2,2) | T_{d} | 0.970698010933 | 0.971016432792 | tetsym.104.txt | tetsym.104.off | tetsym.104.3d | Deeter |

106 | (4,0,2,2) | T | 0.971262846680 | 0.971561731894 | tetsym.106.txt | tetsym.106.off | tetsym.106.3d | Deeter |

108 | (3,1,-2,3) | T | 0.971817587173 | 0.972086891845 | tetsym.108.txt | tetsym.108.off | tetsym.108.3d | Deeter |

110 | (?) | T | 0.972099692997 | 0.972593008064 | tetsym.110.txt | tetsym.110.off | tetsym.110.3d | Deeter |

112 | (1,3,-2,4) | T | 0.972874994894^{ d} | 0.973081097945 | minvol.112.txt | minvol.112.off | minvol.112.3d | Deeter |

114 | (?) | T | 0.973126371366 | 0.973552107682 | tetsym.114.txt | tetsym.114.off | tetsym.114.3d | Deeter |

116 | (2,2,-3,3) | T_{d} | 0.973798323032^{ d} | 0.974006918386 | minvol.116.txt | minvol.116.off | minvol.116.3d | Deeter |

118 | (1,3,-3,3) | T | 0.974231716139 | 0.974446351590 | tetsym.118.txt | tetsym.118.off | tetsym.118.3d | Deeter |

120 | (4,0,-1,3) | T | 0.974580231905 | 0.974871174201 | tetsym.120.txt | tetsym.120.off | tetsym.120.3d | Deeter |

122 | (2,2) | I_{h} | 0.975117621291^{ d} | 0.975282102963 | minvol.122.txt | minvol.122.off | minvol.122.3d | Lengyel, Gáspár & Tarnai |

124 | (4,0,0,3) | T | 0.975459803251 | 0.975679808494 | tetsym.124.txt | tetsym.124.off | tetsym.124.3d | Deeter |

126 | (5,0,1,2) | T | 0.975805064957 | 0.976064918939 | tetsym.126.txt | tetsym.126.off | tetsym.126.3d | Deeter |

128 | (3,3,0,3) | T_{d} | 0.976164263543 | 0.976438023278 | tetsym.128.txt | tetsym.128.off | tetsym.128.3d | Deeter |

130 | (?) | T | 0.976432676242 | 0.976799674332 | tetsym.130.txt | tetsym.130.off | tetsym.130.3d | Deeter |

132 | (3,1) | I | 0.976993221138^{ d} | 0.977150391497 | minvol.132.txt | minvol.132.off | minvol.132.3d | Lengyel, Gáspár & Tarnai |

134 | (4,1,0,3) | T | 0.977270990360 | 0.977490663230 | tetsym.134.txt | tetsym.134.off | tetsym.134.3d | Deeter |

136 | (3,1,-2,4) | T | 0.977667575049^{ d} | 0.977820949322 | minvol.136.txt | minvol.136.off | minvol.136.3d | Deeter |

138 | (2,4,0,4) | T_{d} | 0.977855906073 | 0.978141682969 | tetsym.138.txt | tetsym.138.off | tetsym.138.3d | Deeter |

140 | (1,4,-2,4) | T | 0.978270194291 | 0.978453272668 | tetsym.140.txt | tetsym.140.off | tetsym.140.3d | Deeter |

142 | (4,1,2,3) | T | 0.978520390415 | 0.978756103949 | tetsym.142.txt | tetsym.142.off | tetsym.142.3d | Deeter |

144 | (1,3,-4,3) | T_{h} | 0.978900773049 | 0.979050540972 | tetsym.144.txt | tetsym.144.off | tetsym.144.3d | Deeter |

146 | (?) | T | 0.978962348083 | 0.979336927986 | tetsym.146.txt | tetsym.146.off | tetsym.146.3d | Deeter |

148 | (2,3,-2,4) | T | 0.979461916745 | 0.979615590668 | tetsym.148.txt | tetsym.148.off | tetsym.148.3d | Deeter |

150 | (3,2,-1,4) | T | 0.979740074344^{ d} | 0.979886837362 | minvol.150.txt | minvol.150.off | minvol.150.3d | Deeter |

152 | (1,4,-3,3) | T | 0.979944692488 | 0.980150960218 | tetsym.152.txt | tetsym.152.off | tetsym.152.3d | Deeter |

154 | (4,0,-2,4) | T_{d} | 0.980258341933 | 0.980408236238 | tetsym.154.txt | tetsym.154.off | tetsym.154.3d | Deeter |

156 | (4,0,-1,4) | T | 0.980516728225 | 0.980658928246 | tetsym.156.txt | tetsym.156.off | tetsym.156.3d | Deeter |

158 | (?) | T | 0.980674572726 | 0.980903285786 | tetsym.158.txt | tetsym.158.off | tetsym.158.3d | Deeter |

160 | (3,2,-2,4) | T | 0.980998534842 | 0.981141545948 | tetsym.160.txt | tetsym.160.off | tetsym.160.3d | Deeter |

162 | (4,0) | I_{h} | 0.981238238339 | 0.981373934136 | g_4_0.txt | g_4_0.off | g_4_0.3d | Deeter |

164 | (?) | T | 0.981378870218 | 0.981600664779 | tetsym.164.txt | tetsym.164.off | tetsym.164.3d | Deeter |

166 | (1,4,-3,4) | T | 0.981682473750 | 0.981821941992 | tetsym.166.txt | tetsym.166.off | tetsym.166.3d | Deeter |

168 | (2,3,-3,4) | T | 0.981907852015 | 0.982037960187 | tetsym.168.txt | tetsym.168.off | tetsym.168.3d | Deeter |

170 | (6,0,2,2) | T_{d} | 0.982095063484 | 0.982248904644 | tetsym.170.txt | tetsym.170.off | tetsym.170.3d | Deeter |

172 | (4,1,0,4) | T | 0.982328456340 | 0.982454952041 | tetsym.172.txt | tetsym.172.off | tetsym.172.3d | Deeter |

174 | (2,3,-2,5) | T_{h} | 0.982540234608^{ d} | 0.982656270947 | minvol.174.txt | minvol.174.off | minvol.174.3d | Deeter |

176 | (4,1,1,4) | T_{h} | 0.982716509415 | 0.982853022282 | tetsym.176.txt | tetsym.176.off | tetsym.176.3d | Deeter |

178 | (2,4,-2,4) | T | 0.982889087564 | 0.983045359746 | tetsym.178.txt | tetsym.178.off | tetsym.178.3d | Deeter |

180 | (5,0,2,3) | T | 0.983095400117 | 0.983233430219 | tetsym.180.txt | tetsym.180.off | tetsym.180.3d | Deeter |

182 | (3,3,-3,3) | T_{d} | 0.983211850029 | 0.983417374137 | tetsym.182.txt | tetsym.182.off | tetsym.182.3d | Deeter |

184 | (1,4,-3,5) | T | 0.983486326715^{ d} | 0.983597325839 | minvol.184.txt | minvol.184.off | minvol.184.3d | Deeter |

186 | (4,2,0,4) | T | 0.983645036992 | 0.983773413896 | tetsym.186.txt | tetsym.186.off | tetsym.186.3d | Deeter |

188 | (3,3,-2,4) | T | 0.983794688586 | 0.983945761417 | tetsym.188.txt | tetsym.188.off | tetsym.188.3d | Deeter |

190 | (?) | T | 0.983935609108 | 0.984114486334 | tetsym.190.txt | tetsym.190.off | tetsym.190.3d | Deeter |

192 | (3,2) | I | 0.984183243097^{ d} | 0.984279701676 | minvol.192.txt | minvol.192.off | minvol.192.3d | Deeter |

194 | (?) | T | 0.984290169898 | 0.984441515817 | tetsym.194.txt | tetsym.194.off | tetsym.194.3d | Deeter |

196 | (1,4,-4,4) | T | 0.984489974655 | 0.984600032712 | tetsym.196.txt | tetsym.196.off | tetsym.196.3d | Deeter |

198 | (5,0,-1,4) | T | 0.984618141420 | 0.984755352127 | tetsym.198.txt | tetsym.198.off | tetsym.198.3d | Deeter |

200 | (?) | T | 0.984755760579 | 0.984907569839 | tetsym.200.txt | tetsym.200.off | tetsym.200.3d | Deeter |

202 | (?) | T | 0.984915539017 | 0.985056777840 | tetsym.202.txt | tetsym.202.off | tetsym.202.3d | Deeter |

204 | (3,2,-3,5) | T_{h} | 0.985110848658^{ d} | 0.985203064520 | minvol.204.txt | minvol.204.off | minvol.204.3d | Deeter |

206 | (3,3,-1,5) | T | 0.985239333365 | 0.985346514840 | tetsym.206.txt | tetsym.206.off | tetsym.206.3d | Deeter |

208 | (?) | T | 0.985362104088 | 0.985487210500 | tetsym.208.txt | tetsym.208.off | tetsym.208.3d | Deeter |

210 | (?) | T | 0.985491756662 | 0.985625230090 | tetsym.210.txt | tetsym.210.off | tetsym.210.3d | Deeter |

212 | (4,1) | I | 0.985670055311^{ d} | 0.985760649239 | minvol.212.txt | minvol.212.off | minvol.212.3d | Deeter |

214 | (4,1,-2,5) | T | 0.985803607212^{ d} | 0.985893540755 | minvol.214.txt | minvol.214.off | minvol.214.3d | Deeter |

216 | (5,1,0,4) | T | 0.985912205210 | 0.986023974751 | tetsym.216.txt | tetsym.216.off | tetsym.216.3d | Deeter |

218 | (?) | T | 0.986027899520 | 0.986152018771 | tetsym.218.txt | tetsym.218.off | tetsym.218.3d | Deeter |

220 | (4,1,-3,5) | T | 0.986188260943 | 0.986277737906 | tetsym.220.txt | tetsym.220.off | tetsym.220.3d | Deeter |

222 | (1,5,-3,5) | T | 0.986300575318 | 0.986401194906 | tetsym.222.txt | tetsym.222.off | tetsym.222.3d | Deeter |

224 | (?) | T | 0.986382107090 | 0.986522450281 | tetsym.224.txt | tetsym.224.off | tetsym.224.3d | Deeter |

226 | (?) | T | 0.986518286693 | 0.986641562404 | tetsym.226.txt | tetsym.226.off | tetsym.226.3d | Deeter |

228 | (2,4,-3,5) | T | 0.986669287606 | 0.986758587600 | tetsym.228.txt | tetsym.228.off | tetsym.228.3d | Deeter |

230 | (1,4,-5,4) | T_{h} | 0.986787597502 | 0.986873580241 | tetsym.230.txt | tetsym.230.off | tetsym.230.3d | Deeter |

232 | (4,2,-1,5) | T | 0.986901936464 | 0.986986592823 | tetsym.232.txt | tetsym.232.off | tetsym.232.3d | Deeter |

234 | (2,4,-2,6) | T_{h} | 0.987000936014 | 0.987097676052 | tetsym.234.txt | tetsym.234.off | tetsym.234.3d | Deeter |

236 | (6,0,3,3) | T | 0.987091017806 | 0.987206878916 | tetsym.236.txt | tetsym.236.off | tetsym.236.3d | Deeter |

238 | (3,3,-3,5) | T | 0.987230515744 | 0.987314248760 | tetsym.238.txt | tetsym.238.off | tetsym.238.3d | Deeter |

240 | (4,2,-2,5) | T | 0.987334480474 | 0.987419831350 | tetsym.240.txt | tetsym.240.off | tetsym.240.3d | Deeter |

242 | (?) | T | 0.987379806139 | 0.987523670943 | tetsym.242.txt | tetsym.242.off | tetsym.242.3d | Deeter |

244 | (5,0,-1,5) | T | 0.987544209542 | 0.987625810348 | tetsym.244.txt | tetsym.244.off | tetsym.244.3d | Deeter |

246 | (4,3,0,5) | T | 0.987628375276 | 0.987726290981 | tetsym.246.txt | tetsym.246.off | tetsym.246.3d | Deeter |

248 | (?) | T | 0.987724674695 | 0.987825152924 | tetsym.248.txt | tetsym.248.off | tetsym.248.3d | Deeter |

250 | (?) | T | 0.987825191129 | 0.987922434981 | tetsym.250.txt | tetsym.250.off | tetsym.250.3d | Deeter |

252 | (5,0) | I_{h} | 0.987940777388 | 0.988018174720 | g_5_0.txt | g_5_0.off | g_5_0.3d | Deeter |

254 | (?) | T | 0.987972615551 | 0.988112408533 | tetsym.254.txt | tetsym.254.off | tetsym.254.3d | Deeter |

256 | (2,4,-3,6) | T | 0.988132961605^{ d} | 0.988205171673 | minvol.256.txt | minvol.256.off | minvol.256.3d | Deeter |

258 | (?) | T_{h} | 0.988201798314 | 0.988296498300 | tetsym.258.txt | tetsym.258.off | tetsym.258.3d | Deeter |

260 | (3,3,-4,5) | T | 0.988311155882 | 0.988386421528 | tetsym.260.txt | tetsym.260.off | tetsym.260.3d | Deeter |

262 | (5,1,-1,5) | T | 0.988396448641 | 0.988474973458 | tetsym.262.txt | tetsym.262.off | tetsym.262.3d | Deeter |

264 | (5,1,0,5) | T | 0.988487853689 | 0.988562185219 | tetsym.264.txt | tetsym.264.off | tetsym.264.3d | Deeter |

266 | (?) | T_{d} | 0.988553511509 | 0.988648087008 | tetsym.266.txt | tetsym.266.off | tetsym.266.3d | Deeter |

268 | (2,4,-5,4) | T | 0.988657289466 | 0.988732708119 | tetsym.268.txt | tetsym.268.off | tetsym.268.3d | Deeter |

270 | (5,1,1,5) | T_{h} | 0.988738714579 | 0.988816076980 | tetsym.270.txt | tetsym.270.off | tetsym.270.3d | Deeter |

272 | (3,3) | I_{h} | 0.988834368651^{ d} | 0.988898221182 | minvol.272.txt | minvol.272.off | minvol.272.3d | Deeter |

274 | (6,0,2,4) | T | 0.988900872228 | 0.988979167515 | tetsym.274.txt | tetsym.274.off | tetsym.274.3d | Deeter |

276 | (1,5,-4,6) | T | 0.988990815895^{ d} | 0.989058941990 | minvol.276.txt | minvol.276.off | minvol.276.3d | Deeter |

278 | (7,1,3,3) | T_{d} | 0.989048356130 | 0.989137569871 | tetsym.278.txt | tetsym.278.off | tetsym.278.3d | Deeter |

280 | (5,2,0,5) | T | 0.989140077684 | 0.989215075702 | tetsym.280.txt | tetsym.280.off | tetsym.280.3d | Deeter |

282 | (4,2) | I | 0.989229321481^{ d} | 0.989291483332 | minvol.282.txt | minvol.282.off | minvol.282.3d | Deeter |

284 | (?) | T | 0.989292232927 | 0.989366815936 | tetsym.284.txt | tetsym.284.off | tetsym.284.3d | Deeter |

286 | (3,3,-5,5) | T_{d} | 0.989374814330 | 0.989441096043 | tetsym.286.txt | tetsym.286.off | tetsym.286.3d | Deeter |

288 | (2,4,-5,5) | T | 0.989448432682 | 0.989514345559 | tetsym.288.txt | tetsym.288.off | tetsym.288.3d | Deeter |

290 | (?) | T_{h} | 0.989503498226 | 0.989586585783 | tetsym.290.txt | tetsym.290.off | tetsym.290.3d | Deeter |

292 | (4,2,-3,6) | T | 0.989597321036^{ d} | 0.989657837433 | minvol.292.txt | minvol.292.off | minvol.292.3d | Deeter |

294 | (1,5,-5,5) | T | 0.989662076592 | 0.989728120663 | tetsym.294.txt | tetsym.294.off | tetsym.294.3d | Deeter |

296 | (2,5,-3,6) | T | 0.989729036195 | 0.989797455083 | tetsym.296.txt | tetsym.296.off | tetsym.296.3d | Deeter |

298 | (?) | T | 0.989794897366 | 0.989865859778 | tetsym.298.txt | tetsym.298.off | tetsym.298.3d | Deeter |

300 | (4,3,-1,6) | T | 0.989867862714 | 0.989933353323 | tetsym.300.txt | tetsym.300.off | tetsym.300.3d | Deeter |

302 | (2,5,-4,5) | T | 0.989923885540 | 0.989999953802 | tetsym.302.txt | tetsym.302.off | tetsym.302.3d | Deeter |

304 | (6,0,0,5) | T | 0.989999317330 | 0.990065678825 | tetsym.304.txt | tetsym.304.off | tetsym.304.3d | Deeter |

306 | (4,2,-4,6) | T_{h} | 0.990071329840^{ d} | 0.990130545541 | minvol.306.txt | minvol.306.off | minvol.306.3d | Deeter |

308 | (?) | T | 0.990112688933 | 0.990194570652 | tetsym.308.txt | tetsym.308.off | tetsym.308.3d | Deeter |

310 | (3,4,-3,6) | T | 0.990197685903 | 0.990257770433 | tetsym.310.txt | tetsym.310.off | tetsym.310.3d | Deeter |

312 | (5,1) | I | 0.990262389369^{ d} | 0.990320160740 | minvol.312.txt | minvol.312.off | minvol.312.3d | Deeter |

314 | (4,4,0,6) | T | 0.990297369204 | 0.990381757026 | tetsym.314.txt | tetsym.314.off | tetsym.314.3d | Deeter |

316 | (5,1,-3,6) | T | 0.990383675697 | 0.990442574352 | tetsym.316.txt | tetsym.316.off | tetsym.316.3d | Deeter |

318 | (6,1,0,5) | T | 0.990435787568 | 0.990502627403 | tetsym.318.txt | tetsym.318.off | tetsym.318.3d | Deeter |

320 | (?) | T | 0.990499836991 | 0.990561930495 | tetsym.320.txt | tetsym.320.off | tetsym.320.3d | Deeter |

322 | (?) | T | 0.990558036104 | 0.990620497588 | tetsym.322.txt | tetsym.322.off | tetsym.322.3d | Deeter |

324 | (1,5,-6,4) | T | 0.990620814939 | 0.990678342301 | tetsym.324.txt | tetsym.324.off | tetsym.324.3d | Deeter |

326 | (?) | T | 0.990650117126 | 0.990735477916 | tetsym.326.txt | tetsym.326.off | tetsym.326.3d | Deeter |

328 | (4,3,-3,6) | T | 0.990735205666 | 0.990791917393 | tetsym.328.txt | tetsym.328.off | tetsym.328.3d | Deeter |

330 | (?) | T | 0.990781314581 | 0.990847673377 | tetsym.330.txt | tetsym.330.off | tetsym.330.3d | Deeter |

332 | (5,2,0,6) | T | 0.990844093871 | 0.990902758208 | tetsym.332.txt | tetsym.332.off | tetsym.332.3d | Deeter |

334 | (5,2,-1,6) | T | 0.990902605253 | 0.990957183934 | tetsym.334.txt | tetsym.334.off | tetsym.334.3d | Deeter |

336 | (3,4,-4,6) | T | 0.990956570179 | 0.991010962313 | tetsym.336.txt | tetsym.336.off | tetsym.336.3d | Deeter |

338 | (?) | T | 0.991002173342 | 0.991064104827 | tetsym.338.txt | tetsym.338.off | tetsym.338.3d | Deeter |

340 | (5,2,-2,6) | T | 0.991061160229 | 0.991116622685 | tetsym.340.txt | tetsym.340.off | tetsym.340.3d | Deeter |

342 | (7,0,3,4) | T | 0.991100778885 | 0.991168526839 | tetsym.342.txt | tetsym.342.off | tetsym.342.3d | Deeter |

344 | (6,0,-3,6) | T_{d} | 0.991161789057 | 0.991219827982 | tetsym.344.txt | tetsym.344.off | tetsym.344.3d | Deeter |

346 | (?) | T | 0.991214921913 | 0.991270536562 | tetsym.346.txt | tetsym.346.off | tetsym.346.3d | Deeter |

348 | (3,4,-3,7) | T_{h} | 0.991270860093^{ d} | 0.991320662788 | minvol.348.txt | minvol.348.off | minvol.348.3d | Deeter |

350 | (?) | T | 0.991315374239 | 0.991370216633 | tetsym.350.txt | tetsym.350.off | tetsym.350.3d | Deeter |

352 | (6,0,-1,6) | T | 0.991366819938 | 0.991419207846 | tetsym.352.txt | tetsym.352.off | tetsym.352.3d | Deeter |

354 | (?) | T | 0.991413419037 | 0.991467645955 | tetsym.354.txt | tetsym.354.off | tetsym.354.3d | Deeter |

356 | (?) | T | 0.991456694647 | 0.991515540273 | tetsym.356.txt | tetsym.356.off | tetsym.356.3d | Deeter |

358 | (2,5,-4,7) | T | 0.991514182142^{ d} | 0.991562899908 | minvol.358.txt | minvol.358.off | minvol.358.3d | Deeter |

360 | (?) | T | 0.991557568111 | 0.991609733763 | tetsym.360.txt | tetsym.360.off | tetsym.360.3d | Deeter |

362 | (6,0) | I_{h} | 0.991606177187 | 0.991656050546 | g_6_0.txt | g_6_0.off | g_6_0.3d | Deeter |

364 | (2,5,-5,6) | T | 0.991651886560 | 0.991701858772 | tetsym.364.txt | tetsym.364.off | tetsym.364.3d | Deeter |

366 | (3,4,-5,6) | T | 0.991697812899 | 0.991747166771 | tetsym.366.txt | tetsym.366.off | tetsym.366.3d | Deeter |

368 | (4,4,-3,6) | T | 0.991733264151 | 0.991791982694 | tetsym.368.txt | tetsym.368.off | tetsym.368.3d | Deeter |

370 | (?) | T | 0.991784176066 | 0.991836314512 | tetsym.370.txt | tetsym.370.off | tetsym.370.3d | Deeter |

372 | (4,3) | I | 0.991835514075^{ d} | 0.991880170029 | minvol.372.txt | minvol.372.off | minvol.372.3d | Deeter |

374 | (?) | T | 0.991855816948 | 0.991923556878 | tetsym.374.txt | tetsym.374.off | tetsym.374.3d | Deeter |

376 | (?) | T | 0.991918227620 | 0.991966482533 | tetsym.376.txt | tetsym.376.off | tetsym.376.3d | Deeter |

378 | (?) | T | 0.991961499110 | 0.992008954309 | tetsym.378.txt | tetsym.378.off | tetsym.378.3d | Deeter |

380 | (?) | T | 0.992002910063 | 0.992050979365 | tetsym.380.txt | tetsym.380.off | tetsym.380.3d | Deeter |

382 | (?) | T | 0.992045421425 | 0.992092564714 | tetsym.382.txt | tetsym.382.off | tetsym.382.3d | Deeter |

384 | (?) | T | 0.992084905450 | 0.992133717221 | tetsym.384.txt | tetsym.384.off | tetsym.384.3d | Deeter |

386 | (?) | T | 0.992116356492 | 0.992174443607 | tetsym.386.txt | tetsym.386.off | tetsym.386.3d | Deeter |

388 | (?) | T | 0.992169090258 | 0.992214750458 | tetsym.388.txt | tetsym.388.off | tetsym.388.3d | Deeter |

390 | (4,3,-4,7) | T_{h} | 0.992211631443^{ d} | 0.992254644223 | minvol.390.txt | minvol.390.off | minvol.390.3d | Deeter |

392 | (5,2) | I | 0.992251198083^{ d} | 0.992294131220 | minvol.392.txt | minvol.392.off | minvol.392.3d | Deeter |

394 | (6,2,0,6) | T | 0.992284339046 | 0.992333217639 | tetsym.394.txt | tetsym.394.off | tetsym.394.3d | Deeter |

396 | (?) | T | 0.992327355295 | 0.992371909544 | tetsym.396.txt | tetsym.396.off | tetsym.396.3d | Deeter |

398 | (?) | T_{d} | 0.992349350679 | 0.992410212879 | tetsym.398.txt | tetsym.398.off | tetsym.398.3d | Deeter |

400 | (5,2,-3,7) | T | 0.992405831738^{ d} | 0.992448133466 | minvol.400.txt | minvol.400.off | minvol.400.3d | Deeter |

402 | (?) | T | 0.992441976553 | 0.992485677016 | tetsym.402.txt | tetsym.402.off | tetsym.402.3d | Deeter |

404 | (2,5,-6,6) | T | 0.992478713942 | 0.992522849123 | tetsym.404.txt | tetsym.404.off | tetsym.404.3d | Deeter |

406 | (?) | T | 0.992505998912 | 0.992559655273 | tetsym.406.txt | tetsym.406.off | tetsym.406.3d | Deeter |

408 | (?) | T | 0.992553159082 | 0.992596100843 | tetsym.408.txt | tetsym.408.off | tetsym.408.3d | Deeter |

410 | (?) | T | 0.992571017643 | 0.992632191106 | tetsym.410.txt | tetsym.410.off | tetsym.410.3d | Deeter |

412 | (5,2,-4,7) | T | 0.992625975335 | 0.992667931233 | tetsym.412.txt | tetsym.412.off | tetsym.412.3d | Deeter |

414 | (5,3,-1,7) | T | 0.992659365678 | 0.992703326295 | tetsym.414.txt | tetsym.414.off | tetsym.414.3d | Deeter |

416 | (?) | T | 0.992696459108 | 0.992738381264 | tetsym.416.txt | tetsym.416.off | tetsym.416.3d | Deeter |

418 | (?) | T | 0.992732163015 | 0.992773101020 | tetsym.418.txt | tetsym.418.off | tetsym.418.3d | Deeter |

420 | (?) | T | 0.992766078320 | 0.992807490347 | tetsym.420.txt | tetsym.420.off | tetsym.420.3d | Deeter |

422 | (?) | T | 0.992791232176 | 0.992841553940 | tetsym.422.txt | tetsym.422.off | tetsym.422.3d | Deeter |

424 | (5,3,-2,7) | T | 0.992834483475 | 0.992875296406 | tetsym.424.txt | tetsym.424.off | tetsym.424.3d | Deeter |

426 | (?) | T | 0.992868209453 | 0.992908722263 | tetsym.426.txt | tetsym.426.off | tetsym.426.3d | Deeter |

428 | (5,2,-5,7) | T_{h} | 0.992900871326 | 0.992941835948 | tetsym.428.txt | tetsym.428.off | tetsym.428.3d | Deeter |

430 | (6,1,-2,7) | T | 0.992934509885 | 0.992974641813 | tetsym.430.txt | tetsym.430.off | tetsym.430.3d | Deeter |

432 | (6,1) | I | 0.992967399932 | 0.993007144131 | g_6_1.txt | g_6_1.off | g_6_1.3d | Deeter |

434 | (?) | T | 0.992999116652 | 0.993039347094 | tetsym.434.txt | tetsym.434.off | tetsym.434.3d | Deeter |

436 | (?) | T | 0.993032105841 | 0.993071254821 | tetsym.436.txt | tetsym.436.off | tetsym.436.3d | Deeter |

438 | (5,3,-3,7) | T | 0.993062656884 | 0.993102871352 | tetsym.438.txt | tetsym.438.off | tetsym.438.3d | Deeter |

440 | (7,1,0,6) | T | 0.993089934670 | 0.993134200656 | tetsym.440.txt | tetsym.440.off | tetsym.440.3d | Deeter |

442 | (?) | T | 0.993126879655 | 0.993165246628 | tetsym.442.txt | tetsym.442.off | tetsym.442.3d | Deeter |

444 | (?) | T | 0.993158463816 | 0.993196013096 | tetsym.444.txt | tetsym.444.off | tetsym.444.3d | Deeter |

446 | (?) | T | 0.993187036144 | 0.993226503816 | tetsym.446.txt | tetsym.446.off | tetsym.446.3d | Deeter |

448 | (?) | T | 0.993219766176 | 0.993256722480 | tetsym.448.txt | tetsym.448.off | tetsym.448.3d | Deeter |

450 | (?) | T | 0.993249438426 | 0.993286672712 | tetsym.450.txt | tetsym.450.off | tetsym.450.3d | Deeter |

452 | (?) | T | 0.993278990895 | 0.993316358073 | tetsym.452.txt | tetsym.452.off | tetsym.452.3d | Deeter |

454 | (3,5,-5,7) | T | 0.993307778770 | 0.993345782062 | tetsym.454.txt | tetsym.454.off | tetsym.454.3d | Deeter |

456 | (6,2,-1,7) | T | 0.993337008044 | 0.993374948115 | tetsym.456.txt | tetsym.456.off | tetsym.456.3d | Deeter |

458 | (4,4,-6,6) | T_{d} | 0.993363007678 | 0.993403859609 | tetsym.458.txt | tetsym.458.off | tetsym.458.3d | Deeter |

460 | (?) | T | 0.993396808336 | 0.993432519862 | tetsym.460.txt | tetsym.460.off | tetsym.460.3d | Deeter |

462 | (1,6,-7,6) | T_{h} | 0.993422998248 | 0.993460932136 | tetsym.462.txt | tetsym.462.off | tetsym.462.3d | Deeter |

464 | (4,4,-5,7) | T | 0.993451653061 | 0.993489099633 | tetsym.464.txt | tetsym.464.off | tetsym.464.3d | Deeter |

466 | (?) | T | 0.993480583793 | 0.993517025506 | tetsym.466.txt | tetsym.466.off | tetsym.466.3d | Deeter |

468 | (2,6,-5,8)^{ h} | T | 0.993510193147^{ d} | 0.993544712848 | minvol.468.txt | minvol.468.off | minvol.468.3d | Deeter |

470 | (?) | T | 0.993537392150 | 0.993572164703 | tetsym.470.txt | tetsym.470.off | tetsym.470.3d | Deeter |

472 | (?) | T | 0.993563874338 | 0.993599384063 | tetsym.472.txt | tetsym.472.off | tetsym.472.3d | Deeter |

474 | (?) | T | 0.993588062735 | 0.993626373868 | tetsym.474.txt | tetsym.474.off | tetsym.474.3d | Deeter |

476 | (1,7,-6,6) | T | 0.993611155277 | 0.993653137012 | tetsym.476.txt | tetsym.476.off | tetsym.476.3d | Deeter |

478 | (5,3,-5,7) | T | 0.993642307010 | 0.993679676335 | tetsym.478.txt | tetsym.478.off | tetsym.478.3d | Deeter |

480 | (?) | T | 0.993672332016 | 0.993705994636 | tetsym.480.txt | tetsym.480.off | tetsym.480.3d | Deeter |

482 | (4,4) | I | 0.993698846507 | 0.993732094664 | g_4_4.txt | g_4_4.off | g_4_4.3d | Deeter |

484 | (?) | T | 0.993724404971 | 0.993757979121 | tetsym.484.txt | tetsym.484.off | tetsym.484.3d | Deeter |

486 | (4,5,-4,7) | T | 0.993743040716 | 0.993783650670 | tetsym.486.txt | tetsym.486.off | tetsym.486.3d | Deeter |

488 | (?) | T | 0.993773725718 | 0.993809111924 | tetsym.488.txt | tetsym.488.off | tetsym.488.3d | Deeter |

490 | (?) | T | 0.993800964567 | 0.993834365459 | tetsym.490.txt | tetsym.490.off | tetsym.490.3d | Deeter |

492 | (4,5,-3,8)^{ h} | T | 0.993826897052 | 0.993859413805 | tetsym.492.txt | tetsym.492.off | tetsym.492.3d | Deeter |

494 | (?) | T | 0.993845459822 | 0.993884259454 | tetsym.494.txt | tetsym.494.off | tetsym.494.3d | Deeter |

496 | (?) | T | 0.993877008121 | 0.993908904855 | tetsym.496.txt | tetsym.496.off | tetsym.496.3d | Deeter |

498 | (?) | T | 0.993895644739 | 0.993933352420 | tetsym.498.txt | tetsym.498.off | tetsym.498.3d | Deeter |

500 | (?) | T | 0.993926124084 | 0.993957604521 | tetsym.500.txt | tetsym.500.off | tetsym.500.3d | Deeter |

502 | (7,1,-1,7) | T | 0.993946231032 | 0.993981663494 | tetsym.502.txt | tetsym.502.off | tetsym.502.3d | Deeter |

512 | (?) | T_{h} | 0.994065066201 | 0.994099140595 | tetsym.512.txt | tetsym.512.off | tetsym.512.3d | Deeter |

^{a} Face normals are provided as an unordered list of the tangent points in
N. J. A. Sloane's future-proof format: each point's *X*, *Y* and *Z*
coordinates are on three consecutive lines in the file.
^{b} Polyhedra are provided in the simple *OFF* polyhedron format.
The first line is the literal "OFF". The second line is three space separated integers
for the number of vertices, number of faces, and number of edges of the polyhedron.
The next lines are the *X*, *Y* and *Z* coordinates of the polyhedron vertices.
Finally are lines for each of the polyhedron faces, lists of space separated integers.
The first on each line is the number of sides of the polygon, followed by that number of
zero-based indices into the preceding list of vertices, in counter-clockwise order.
^{c} Proven best regardless of symmetry.
^{d} Best known regardless of symmetry.
^{e} Without faces with normals at the octahedron vertices.
^{f} With pyramidal caps replacing the six square faces.
^{g} With additional face normals added by projecting centroids of the regular octahedron's
faces.
^{h} With face normals of 12 pentagon-heptagon pairs replaced by a single normal midway
between.
^{i} Uses Phoria javascript package from http://www.kevs3d.co.uk/dev/phoria/ to display
polyhedra.
^{j} Octahedral Goldberg (1,1) with single or double truncations of alternate vertices.
^{k} Started with Fowler-Cremona-Steer (1,4,-1,2), degenerated to O_{h} when optimized
for IQ.

n | G | IQ | upper bound | normals | polyhedron | model |
---|---|---|---|---|---|---|

504 | (4,5,-3,8) | 0.993970792763 | 0.994005531636 | tetsym.504.txt | tetsym.504.off | tetsym.504.3d |

^{a} Identical polyhedra generated from different Goldberg polyhedra.

Wayne Deeter - wrd@deetour.net

Last modified: April 23, 2018