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# Polytope of Type {2,2,2,4}

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

```
Permutation Representation (Magma) :
```s0 := Sym(10)!(1,2);
s1 := Sym(10)!(3,4);
s2 := Sym(10)!(5,6);
s3 := Sym(10)!(8,9);
s4 := Sym(10)!( 7, 8)( 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*s1*s0*s1, 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*s3*s4*s3*s4 >;

```

to this polytope