Polytope of Type {4,2,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,2}*64
if this polytope has a name.
Group : SmallGroup(64,261)
Rank : 5
Schlafli Type : {4,2,2,2}
Number of vertices, edges, etc : 4, 4, 2, 2, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,2,2,2} of size 128
{4,2,2,2,3} of size 192
{4,2,2,2,4} of size 256
{4,2,2,2,5} of size 320
{4,2,2,2,6} of size 384
{4,2,2,2,7} of size 448
{4,2,2,2,8} of size 512
{4,2,2,2,9} of size 576
{4,2,2,2,10} of size 640
{4,2,2,2,11} of size 704
{4,2,2,2,12} of size 768
{4,2,2,2,13} of size 832
{4,2,2,2,14} of size 896
{4,2,2,2,15} of size 960
{4,2,2,2,17} of size 1088
{4,2,2,2,18} of size 1152
{4,2,2,2,19} of size 1216
{4,2,2,2,20} of size 1280
{4,2,2,2,21} of size 1344
{4,2,2,2,22} of size 1408
{4,2,2,2,23} of size 1472
{4,2,2,2,25} of size 1600
{4,2,2,2,26} of size 1664
{4,2,2,2,27} of size 1728
{4,2,2,2,28} of size 1792
{4,2,2,2,29} of size 1856
{4,2,2,2,30} of size 1920
{4,2,2,2,31} of size 1984
Vertex Figure Of :
{2,4,2,2,2} of size 128
{3,4,2,2,2} of size 192
{4,4,2,2,2} of size 256
{6,4,2,2,2} of size 384
{3,4,2,2,2} of size 384
{6,4,2,2,2} of size 384
{6,4,2,2,2} of size 384
{8,4,2,2,2} of size 512
{8,4,2,2,2} of size 512
{4,4,2,2,2} of size 512
{9,4,2,2,2} of size 576
{4,4,2,2,2} of size 576
{6,4,2,2,2} of size 576
{10,4,2,2,2} of size 640
{12,4,2,2,2} of size 768
{12,4,2,2,2} of size 768
{12,4,2,2,2} of size 768
{6,4,2,2,2} of size 768
{14,4,2,2,2} of size 896
{5,4,2,2,2} of size 960
{6,4,2,2,2} of size 960
{15,4,2,2,2} of size 960
{18,4,2,2,2} of size 1152
{4,4,2,2,2} of size 1152
{6,4,2,2,2} of size 1152
{9,4,2,2,2} of size 1152
{18,4,2,2,2} of size 1152
{18,4,2,2,2} of size 1152
{20,4,2,2,2} of size 1280
{5,4,2,2,2} of size 1280
{21,4,2,2,2} of size 1344
{22,4,2,2,2} of size 1408
{4,4,2,2,2} of size 1600
{10,4,2,2,2} of size 1600
{26,4,2,2,2} of size 1664
{27,4,2,2,2} of size 1728
{6,4,2,2,2} of size 1728
{12,4,2,2,2} of size 1728
{28,4,2,2,2} of size 1792
{30,4,2,2,2} of size 1920
{15,4,2,2,2} of size 1920
{30,4,2,2,2} of size 1920
{30,4,2,2,2} of size 1920
{5,4,2,2,2} of size 1920
{6,4,2,2,2} of size 1920
{6,4,2,2,2} of size 1920
{6,4,2,2,2} of size 1920
{10,4,2,2,2} of size 1920
{10,4,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,2,2}*128, {4,2,2,4}*128, {4,2,4,2}*128, {8,2,2,2}*128
3-fold covers : {12,2,2,2}*192, {4,2,2,6}*192, {4,2,6,2}*192, {4,6,2,2}*192a
4-fold covers : {4,4,4,2}*256, {4,2,4,4}*256, {4,4,2,4}*256, {4,8,2,2}*256a, {8,4,2,2}*256a, {4,8,2,2}*256b, {8,4,2,2}*256b, {4,4,2,2}*256, {4,2,2,8}*256, {4,2,8,2}*256, {8,2,2,4}*256, {8,2,4,2}*256, {16,2,2,2}*256
5-fold covers : {20,2,2,2}*320, {4,2,2,10}*320, {4,2,10,2}*320, {4,10,2,2}*320
6-fold covers : {4,12,2,2}*384a, {12,4,2,2}*384a, {4,2,2,12}*384, {4,2,12,2}*384, {12,2,2,4}*384, {12,2,4,2}*384, {4,4,2,6}*384, {4,4,6,2}*384, {4,6,4,2}*384a, {4,2,4,6}*384a, {4,2,6,4}*384a, {4,6,2,4}*384a, {24,2,2,2}*384, {8,2,2,6}*384, {8,2,6,2}*384, {8,6,2,2}*384
7-fold covers : {28,2,2,2}*448, {4,2,2,14}*448, {4,2,14,2}*448, {4,14,2,2}*448
8-fold covers : {4,4,4,4}*512, {4,8,2,2}*512a, {8,4,2,2}*512a, {8,8,2,2}*512a, {8,8,2,2}*512b, {8,8,2,2}*512c, {8,8,2,2}*512d, {8,2,2,8}*512, {8,2,8,2}*512, {4,8,4,2}*512a, {4,8,4,2}*512b, {4,8,4,2}*512c, {4,8,4,2}*512d, {4,4,8,2}*512a, {8,4,4,2}*512a, {4,4,8,2}*512b, {8,4,4,2}*512b, {4,4,4,2}*512a, {4,4,4,2}*512b, {4,16,2,2}*512a, {16,4,2,2}*512a, {4,16,2,2}*512b, {16,4,2,2}*512b, {4,4,2,2}*512, {4,8,2,2}*512b, {8,4,2,2}*512b, {4,2,2,16}*512, {4,2,16,2}*512, {16,2,2,4}*512, {16,2,4,2}*512, {32,2,2,2}*512
9-fold covers : {36,2,2,2}*576, {4,2,2,18}*576, {4,2,18,2}*576, {4,18,2,2}*576a, {12,2,2,6}*576, {12,2,6,2}*576, {12,6,2,2}*576a, {12,6,2,2}*576b, {4,2,6,6}*576a, {4,2,6,6}*576b, {4,2,6,6}*576c, {4,6,2,6}*576a, {4,6,6,2}*576a, {4,6,6,2}*576b, {4,6,6,2}*576c, {12,6,2,2}*576c, {4,6,2,2}*576
10-fold covers : {4,20,2,2}*640, {20,4,2,2}*640, {4,2,2,20}*640, {4,2,20,2}*640, {20,2,2,4}*640, {20,2,4,2}*640, {4,4,2,10}*640, {4,4,10,2}*640, {4,10,4,2}*640, {4,2,4,10}*640, {4,2,10,4}*640, {4,10,2,4}*640, {40,2,2,2}*640, {8,2,2,10}*640, {8,2,10,2}*640, {8,10,2,2}*640
11-fold covers : {44,2,2,2}*704, {4,2,2,22}*704, {4,2,22,2}*704, {4,22,2,2}*704
12-fold covers : {4,4,4,6}*768, {4,4,12,2}*768, {12,4,4,2}*768, {4,12,4,2}*768a, {4,4,6,4}*768a, {4,6,4,4}*768a, {4,4,2,12}*768, {12,2,4,4}*768, {4,2,4,12}*768a, {4,2,12,4}*768a, {4,12,2,4}*768a, {12,4,2,4}*768a, {4,8,2,6}*768a, {4,8,6,2}*768a, {8,4,2,6}*768a, {8,4,6,2}*768a, {8,12,2,2}*768a, {12,8,2,2}*768a, {4,24,2,2}*768a, {24,4,2,2}*768a, {4,8,2,6}*768b, {4,8,6,2}*768b, {8,4,2,6}*768b, {8,4,6,2}*768b, {8,12,2,2}*768b, {12,8,2,2}*768b, {4,24,2,2}*768b, {24,4,2,2}*768b, {4,4,2,6}*768, {4,4,6,2}*768a, {4,12,2,2}*768a, {12,4,2,2}*768a, {4,2,6,8}*768, {4,2,8,6}*768, {4,6,2,8}*768a, {8,2,4,6}*768a, {8,2,6,4}*768a, {8,6,2,4}*768, {4,6,8,2}*768a, {8,6,4,2}*768a, {8,2,2,12}*768, {8,2,12,2}*768, {12,2,2,8}*768, {12,2,8,2}*768, {4,2,2,24}*768, {4,2,24,2}*768, {24,2,2,4}*768, {24,2,4,2}*768, {16,2,2,6}*768, {16,2,6,2}*768, {16,6,2,2}*768, {48,2,2,2}*768, {12,4,2,2}*768b, {4,2,4,6}*768, {4,2,6,4}*768, {4,2,6,6}*768, {4,4,6,2}*768d, {4,6,2,2}*768b, {4,6,4,2}*768a, {4,6,6,2}*768, {12,6,2,2}*768a
13-fold covers : {52,2,2,2}*832, {4,2,2,26}*832, {4,2,26,2}*832, {4,26,2,2}*832
14-fold covers : {4,28,2,2}*896, {28,4,2,2}*896, {4,2,2,28}*896, {4,2,28,2}*896, {28,2,2,4}*896, {28,2,4,2}*896, {4,4,2,14}*896, {4,4,14,2}*896, {4,14,4,2}*896, {4,2,4,14}*896, {4,2,14,4}*896, {4,14,2,4}*896, {56,2,2,2}*896, {8,2,2,14}*896, {8,2,14,2}*896, {8,14,2,2}*896
15-fold covers : {12,2,2,10}*960, {12,2,10,2}*960, {12,10,2,2}*960, {20,2,2,6}*960, {20,2,6,2}*960, {20,6,2,2}*960a, {4,2,6,10}*960, {4,2,10,6}*960, {4,6,2,10}*960a, {4,6,10,2}*960a, {4,10,2,6}*960, {4,10,6,2}*960, {60,2,2,2}*960, {4,2,2,30}*960, {4,2,30,2}*960, {4,30,2,2}*960a
17-fold covers : {4,2,2,34}*1088, {4,2,34,2}*1088, {4,34,2,2}*1088, {68,2,2,2}*1088
18-fold covers : {4,4,2,18}*1152, {4,4,18,2}*1152, {4,36,2,2}*1152a, {36,4,2,2}*1152a, {4,4,6,6}*1152a, {4,4,6,6}*1152b, {4,4,6,6}*1152c, {4,12,2,6}*1152a, {4,12,6,2}*1152a, {4,12,6,2}*1152b, {12,4,2,6}*1152a, {12,4,6,2}*1152, {4,12,6,2}*1152c, {12,12,2,2}*1152a, {12,12,2,2}*1152b, {12,12,2,2}*1152c, {4,4,2,2}*1152, {4,4,6,2}*1152, {4,12,2,2}*1152, {12,4,2,2}*1152, {4,2,4,18}*1152a, {4,2,18,4}*1152a, {4,18,2,4}*1152a, {4,18,4,2}*1152a, {4,2,2,36}*1152, {4,2,36,2}*1152, {36,2,2,4}*1152, {36,2,4,2}*1152, {4,6,4,6}*1152a, {4,6,6,4}*1152a, {4,6,6,4}*1152b, {4,6,6,4}*1152c, {4,2,6,12}*1152a, {4,2,12,6}*1152a, {12,6,2,4}*1152a, {4,2,6,12}*1152b, {4,2,6,12}*1152c, {4,2,12,6}*1152b, {4,2,12,6}*1152c, {4,6,2,12}*1152a, {12,2,4,6}*1152a, {12,2,6,4}*1152a, {12,6,2,4}*1152b, {12,6,2,4}*1152c, {4,6,12,2}*1152a, {12,6,4,2}*1152a, {4,6,12,2}*1152b, {12,6,4,2}*1152b, {4,6,12,2}*1152c, {12,6,4,2}*1152c, {12,2,2,12}*1152, {12,2,12,2}*1152, {4,2,4,4}*1152, {4,2,4,6}*1152, {4,2,6,4}*1152, {4,4,4,2}*1152b, {4,6,2,4}*1152, {4,6,4,2}*1152a, {4,6,4,2}*1152b, {8,2,2,18}*1152, {8,2,18,2}*1152, {8,18,2,2}*1152, {72,2,2,2}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152b, {8,2,6,6}*1152c, {8,6,2,6}*1152, {8,6,6,2}*1152a, {8,6,6,2}*1152b, {8,6,6,2}*1152c, {24,6,2,2}*1152a, {24,2,2,6}*1152, {24,2,6,2}*1152, {24,6,2,2}*1152b, {24,6,2,2}*1152c, {8,6,2,2}*1152
19-fold covers : {4,2,2,38}*1216, {4,2,38,2}*1216, {4,38,2,2}*1216, {76,2,2,2}*1216
20-fold covers : {4,4,4,10}*1280, {4,4,20,2}*1280, {20,4,4,2}*1280, {4,20,4,2}*1280, {4,4,10,4}*1280, {4,10,4,4}*1280, {4,4,2,20}*1280, {20,2,4,4}*1280, {4,2,4,20}*1280, {4,2,20,4}*1280, {4,20,2,4}*1280, {20,4,2,4}*1280, {4,8,2,10}*1280a, {4,8,10,2}*1280a, {8,4,2,10}*1280a, {8,4,10,2}*1280a, {8,20,2,2}*1280a, {20,8,2,2}*1280a, {4,40,2,2}*1280a, {40,4,2,2}*1280a, {4,8,2,10}*1280b, {4,8,10,2}*1280b, {8,4,2,10}*1280b, {8,4,10,2}*1280b, {8,20,2,2}*1280b, {20,8,2,2}*1280b, {4,40,2,2}*1280b, {40,4,2,2}*1280b, {4,4,2,10}*1280, {4,4,10,2}*1280, {4,20,2,2}*1280, {20,4,2,2}*1280, {4,2,8,10}*1280, {4,2,10,8}*1280, {4,10,2,8}*1280, {8,2,4,10}*1280, {8,2,10,4}*1280, {8,10,2,4}*1280, {4,10,8,2}*1280, {8,10,4,2}*1280, {8,2,2,20}*1280, {8,2,20,2}*1280, {20,2,2,8}*1280, {20,2,8,2}*1280, {4,2,2,40}*1280, {4,2,40,2}*1280, {40,2,2,4}*1280, {40,2,4,2}*1280, {16,2,2,10}*1280, {16,2,10,2}*1280, {16,10,2,2}*1280, {80,2,2,2}*1280
21-fold covers : {12,2,2,14}*1344, {12,2,14,2}*1344, {12,14,2,2}*1344, {28,2,2,6}*1344, {28,2,6,2}*1344, {28,6,2,2}*1344a, {4,2,6,14}*1344, {4,2,14,6}*1344, {4,6,2,14}*1344a, {4,6,14,2}*1344a, {4,14,2,6}*1344, {4,14,6,2}*1344, {84,2,2,2}*1344, {4,2,2,42}*1344, {4,2,42,2}*1344, {4,42,2,2}*1344a
22-fold covers : {4,4,2,22}*1408, {4,4,22,2}*1408, {4,44,2,2}*1408, {44,4,2,2}*1408, {4,2,4,22}*1408, {4,2,22,4}*1408, {4,22,2,4}*1408, {4,22,4,2}*1408, {4,2,2,44}*1408, {4,2,44,2}*1408, {44,2,2,4}*1408, {44,2,4,2}*1408, {8,2,2,22}*1408, {8,2,22,2}*1408, {8,22,2,2}*1408, {88,2,2,2}*1408
23-fold covers : {4,2,2,46}*1472, {4,2,46,2}*1472, {4,46,2,2}*1472, {92,2,2,2}*1472
25-fold covers : {100,2,2,2}*1600, {4,2,2,50}*1600, {4,2,50,2}*1600, {4,50,2,2}*1600, {20,2,2,10}*1600, {20,2,10,2}*1600, {20,10,2,2}*1600a, {20,10,2,2}*1600b, {4,2,10,10}*1600a, {4,2,10,10}*1600b, {4,2,10,10}*1600c, {4,10,2,10}*1600, {4,10,10,2}*1600a, {4,10,10,2}*1600b, {4,10,10,2}*1600c, {20,10,2,2}*1600c, {4,10,2,2}*1600
26-fold covers : {4,4,2,26}*1664, {4,4,26,2}*1664, {4,52,2,2}*1664, {52,4,2,2}*1664, {4,2,4,26}*1664, {4,2,26,4}*1664, {4,26,2,4}*1664, {4,26,4,2}*1664, {4,2,2,52}*1664, {4,2,52,2}*1664, {52,2,2,4}*1664, {52,2,4,2}*1664, {8,2,2,26}*1664, {8,2,26,2}*1664, {8,26,2,2}*1664, {104,2,2,2}*1664
27-fold covers : {108,2,2,2}*1728, {4,2,2,54}*1728, {4,2,54,2}*1728, {4,54,2,2}*1728a, {12,2,2,18}*1728, {12,2,18,2}*1728, {12,18,2,2}*1728a, {36,2,2,6}*1728, {36,2,6,2}*1728, {36,6,2,2}*1728a, {36,6,2,2}*1728b, {12,6,2,2}*1728a, {12,6,2,2}*1728b, {12,6,6,2}*1728a, {4,2,6,18}*1728a, {4,2,6,18}*1728b, {4,2,18,6}*1728a, {4,2,18,6}*1728b, {4,6,2,18}*1728a, {4,6,18,2}*1728a, {4,18,2,6}*1728a, {4,18,6,2}*1728a, {4,18,6,2}*1728b, {4,6,6,6}*1728a, {4,2,6,6}*1728a, {4,2,6,6}*1728b, {4,2,6,6}*1728c, {4,6,6,2}*1728a, {4,6,6,2}*1728b, {4,6,18,2}*1728b, {12,18,2,2}*1728b, {4,6,6,2}*1728c, {12,6,2,2}*1728c, {4,6,2,2}*1728a, {12,6,2,2}*1728e, {12,6,2,2}*1728f, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,2,6,6}*1728c, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {12,6,6,2}*1728b, {12,6,6,2}*1728c, {12,6,6,2}*1728d, {4,6,6,6}*1728d, {4,6,6,6}*1728e, {4,6,6,6}*1728f, {4,2,6,6}*1728d, {12,6,2,2}*1728g, {12,6,6,2}*1728e, {4,6,6,6}*1728g, {4,6,6,6}*1728h, {4,6,6,2}*1728h, {12,6,2,6}*1728c, {12,6,6,2}*1728f, {12,6,6,2}*1728g, {4,6,6,6}*1728i, {4,6,2,2}*1728b, {4,6,2,6}*1728, {4,6,6,2}*1728j, {4,6,6,2}*1728k, {12,6,2,2}*1728h, {12,6,2,2}*1728i
28-fold covers : {4,4,4,14}*1792, {4,4,28,2}*1792, {28,4,4,2}*1792, {4,28,4,2}*1792, {4,4,14,4}*1792, {4,14,4,4}*1792, {4,4,2,28}*1792, {28,2,4,4}*1792, {4,2,4,28}*1792, {4,2,28,4}*1792, {4,28,2,4}*1792, {28,4,2,4}*1792, {4,8,2,14}*1792a, {4,8,14,2}*1792a, {8,4,2,14}*1792a, {8,4,14,2}*1792a, {8,28,2,2}*1792a, {28,8,2,2}*1792a, {4,56,2,2}*1792a, {56,4,2,2}*1792a, {4,8,2,14}*1792b, {4,8,14,2}*1792b, {8,4,2,14}*1792b, {8,4,14,2}*1792b, {8,28,2,2}*1792b, {28,8,2,2}*1792b, {4,56,2,2}*1792b, {56,4,2,2}*1792b, {4,4,2,14}*1792, {4,4,14,2}*1792, {4,28,2,2}*1792, {28,4,2,2}*1792, {4,2,8,14}*1792, {4,2,14,8}*1792, {4,14,2,8}*1792, {8,2,4,14}*1792, {8,2,14,4}*1792, {8,14,2,4}*1792, {4,14,8,2}*1792, {8,14,4,2}*1792, {8,2,2,28}*1792, {8,2,28,2}*1792, {28,2,2,8}*1792, {28,2,8,2}*1792, {4,2,2,56}*1792, {4,2,56,2}*1792, {56,2,2,4}*1792, {56,2,4,2}*1792, {16,2,2,14}*1792, {16,2,14,2}*1792, {16,14,2,2}*1792, {112,2,2,2}*1792
29-fold covers : {4,2,2,58}*1856, {4,2,58,2}*1856, {4,58,2,2}*1856, {116,2,2,2}*1856
30-fold covers : {4,4,2,30}*1920, {4,4,30,2}*1920, {4,60,2,2}*1920a, {60,4,2,2}*1920a, {4,4,6,10}*1920, {4,4,10,6}*1920, {4,12,2,10}*1920a, {4,12,10,2}*1920a, {12,4,2,10}*1920a, {12,4,10,2}*1920, {4,20,2,6}*1920, {4,20,6,2}*1920, {20,4,2,6}*1920, {20,4,6,2}*1920, {12,20,2,2}*1920, {20,12,2,2}*1920, {4,2,4,30}*1920a, {4,2,30,4}*1920a, {4,30,2,4}*1920a, {4,30,4,2}*1920a, {4,2,2,60}*1920, {4,2,60,2}*1920, {60,2,2,4}*1920, {60,2,4,2}*1920, {4,6,4,10}*1920a, {4,6,10,4}*1920a, {4,10,6,4}*1920a, {4,10,4,6}*1920, {4,2,10,12}*1920, {4,2,12,10}*1920, {4,10,2,12}*1920, {12,2,4,10}*1920, {12,2,10,4}*1920, {12,10,2,4}*1920, {4,2,6,20}*1920a, {4,2,20,6}*1920a, {4,6,2,20}*1920a, {20,2,4,6}*1920a, {20,2,6,4}*1920a, {20,6,2,4}*1920a, {4,10,12,2}*1920, {12,10,4,2}*1920, {4,6,20,2}*1920a, {20,6,4,2}*1920a, {12,2,2,20}*1920, {12,2,20,2}*1920, {20,2,2,12}*1920, {20,2,12,2}*1920, {8,2,2,30}*1920, {8,2,30,2}*1920, {8,30,2,2}*1920, {120,2,2,2}*1920, {8,2,6,10}*1920, {8,2,10,6}*1920, {8,6,2,10}*1920, {8,6,10,2}*1920, {8,10,2,6}*1920, {8,10,6,2}*1920, {24,2,2,10}*1920, {24,2,10,2}*1920, {24,10,2,2}*1920, {40,2,2,6}*1920, {40,2,6,2}*1920, {40,6,2,2}*1920
31-fold covers : {4,2,2,62}*1984, {4,2,62,2}*1984, {4,62,2,2}*1984, {124,2,2,2}*1984
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := ( 9,10);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(10)!(2,3);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!(5,6);
s3 := Sym(10)!(7,8);
s4 := Sym(10)!( 9,10);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope