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Groups of Size 1728
This page is part of the Atlas of Small Regular Polytopes
176 groups yielding 765 nondegenerate and 2217 degenerate polytopes.
Rank 2 Polytopes : 1 nondegenerate and 0 degenerate.
Rank 3 Polytopes : 302 nondegenerate and
2 degenerate.
Rank 4 Polytopes : 344 nondegenerate and
203 degenerate.
Rank 5 Polytopes : 117 nondegenerate and
672 degenerate.
Rank 6 Polytopes : 1 nondegenerate and
748 degenerate.
Rank 7 Polytopes : 0 nondegenerate and
427 degenerate.
Rank 8 Polytopes : 0 nondegenerate and
145 degenerate.
Rank 9 Polytopes : 0 nondegenerate and 20 degenerate.
Groups :
- SmallGroup(1728,8) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,302) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,309) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,315) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,342) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,390) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,472) 0 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,478) 2 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,2197) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,2198) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,2203) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,2289) 0 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,2353) 0 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,2390) 2 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,2392) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,2542) 0 nondegenerate polytopes and
3 degenerate polytopes.
- SmallGroup(1728,2555) 0 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,3030) 4 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,3040) 2 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,3073) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,3359) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,3511) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,3530) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,3538) 3 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,3898) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,4110) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,4714) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,4743) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5113) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5197) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5217) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5273) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5288) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,5302) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,11356) 2 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,11358) 8 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,11367) 2 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,11371) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,11398) 0 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,11400) 0 nondegenerate polytopes and
24 degenerate polytopes.
- SmallGroup(1728,12249) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12315) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12317) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12518) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12630) 8 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12653) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12703) 16 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12713) 10 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,12762) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,13777) 0 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,13967) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,14196) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,14352) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,14460) 4 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,14461) 6 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,14710) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,14771) 8 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,15813) 0 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,15830) 0 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,15888) 2 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,15957) 8 nondegenerate polytopes and
18 degenerate polytopes.
- SmallGroup(1728,15977) 7 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,16615) 0 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,16621) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,16947) 0 nondegenerate polytopes and
6 degenerate polytopes.
- SmallGroup(1728,16950) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,17171) 2 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,17257) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,17334) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,17452) 2 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,17531) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,17566) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,18104) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,18160) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,20782) 0 nondegenerate polytopes and
30 degenerate polytopes.
- SmallGroup(1728,20783) 6 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,20787) 0 nondegenerate polytopes and
11 degenerate polytopes.
- SmallGroup(1728,21263) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,21860) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,21980) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,23054) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,30173) 6 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,30174) 10 nondegenerate polytopes and
6 degenerate polytopes.
- SmallGroup(1728,30184) 2 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,30189) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30201) 8 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,30216) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30228) 12 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,30229) 8 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,30242) 16 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30243) 12 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30249) 2 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,30258) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30267) 4 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,30272) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30284) 6 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,30298) 12 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30313) 10 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30326) 14 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,30374) 0 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,30394) 10 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,30413) 6 nondegenerate polytopes and
28 degenerate polytopes.
- SmallGroup(1728,30763) 0 nondegenerate polytopes and
24 degenerate polytopes.
- SmallGroup(1728,30764) 0 nondegenerate polytopes and
30 degenerate polytopes.
- SmallGroup(1728,30782) 0 nondegenerate polytopes and
22 degenerate polytopes.
- SmallGroup(1728,30790) 0 nondegenerate polytopes and
104 degenerate polytopes.
- SmallGroup(1728,30804) 2 nondegenerate polytopes and
48 degenerate polytopes.
- SmallGroup(1728,30872) 0 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,30882) 0 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,31257) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31258) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31293) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31294) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31412) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31593) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31623) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,31633) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33416) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33548) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33554) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33596) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33616) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33667) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,33799) 10 nondegenerate polytopes and
15 degenerate polytopes.
- SmallGroup(1728,36607) 2 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,36990) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,36991) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,36999) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,37586) 10 nondegenerate polytopes and
6 degenerate polytopes.
- SmallGroup(1728,37587) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,37593) 12 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,37597) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,38382) 0 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,38764) 1 nondegenerate polytope and
0 degenerate polytopes.
- SmallGroup(1728,38778) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,38784) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,38805) 2 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46098) 10 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,46099) 9 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46100) 10 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46101) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46114) 6 nondegenerate polytopes and
156 degenerate polytopes.
- SmallGroup(1728,46115) 6 nondegenerate polytopes and
134 degenerate polytopes.
- SmallGroup(1728,46116) 14 nondegenerate polytopes and
88 degenerate polytopes.
- SmallGroup(1728,46117) 2 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,46118) 4 nondegenerate polytopes and
2 degenerate polytopes.
- SmallGroup(1728,46119) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46139) 0 nondegenerate polytopes and
56 degenerate polytopes.
- SmallGroup(1728,46164) 0 nondegenerate polytopes and
108 degenerate polytopes.
- SmallGroup(1728,46165) 0 nondegenerate polytopes and
43 degenerate polytopes.
- SmallGroup(1728,46303) 12 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,46304) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46313) 3 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46344) 10 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46356) 14 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46549) 4 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,46587) 6 nondegenerate polytopes and
6 degenerate polytopes.
- SmallGroup(1728,46611) 2 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,46634) 2 nondegenerate polytopes and
12 degenerate polytopes.
- SmallGroup(1728,46671) 16 nondegenerate polytopes and
10 degenerate polytopes.
- SmallGroup(1728,46672) 6 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,46674) 4 nondegenerate polytopes and
0 degenerate polytopes.
- SmallGroup(1728,47196) 0 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,47215) 2 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,47234) 2 nondegenerate polytopes and
8 degenerate polytopes.
- SmallGroup(1728,47319) 0 nondegenerate polytopes and
88 degenerate polytopes.
- SmallGroup(1728,47341) 10 nondegenerate polytopes and
48 degenerate polytopes.
- SmallGroup(1728,47394) 0 nondegenerate polytopes and
16 degenerate polytopes.
- SmallGroup(1728,47409) 6 nondegenerate polytopes and
60 degenerate polytopes.
- SmallGroup(1728,47410) 2 nondegenerate polytopes and
4 degenerate polytopes.
- SmallGroup(1728,47847) 22 nondegenerate polytopes and
18 degenerate polytopes.
- SmallGroup(1728,47870) 7 nondegenerate polytopes and
10 degenerate polytopes.
- SmallGroup(1728,47874) 56 nondegenerate polytopes and
314 degenerate polytopes.
- SmallGroup(1728,47887) 0 nondegenerate polytopes and
124 degenerate polytopes.
- SmallGroup(1728,47912) 0 nondegenerate polytopes and
14 degenerate polytopes.
- SmallGroup(1728,47915) 0 nondegenerate polytopes and
215 degenerate polytopes.