Questions?
See the FAQ
or other info.

# Polytope of Type {2,2,2,3}

Atlas Canonical Name : {2,2,2,3}*48
if this polytope has a name.
Group : SmallGroup(48,51)
Rank : 5
Schlafli Type : {2,2,2,3}
Number of vertices, edges, etc : 2, 2, 2, 3, 3
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,3,2} of size 96
{2,2,2,3,3} of size 192
{2,2,2,3,4} of size 192
{2,2,2,3,6} of size 288
{2,2,2,3,4} of size 384
{2,2,2,3,6} of size 384
{2,2,2,3,5} of size 480
{2,2,2,3,8} of size 768
{2,2,2,3,12} of size 768
{2,2,2,3,6} of size 864
{2,2,2,3,5} of size 960
{2,2,2,3,10} of size 960
{2,2,2,3,10} of size 960
{2,2,2,3,6} of size 1152
{2,2,2,3,12} of size 1152
{2,2,2,3,10} of size 1920
Vertex Figure Of :
{2,2,2,2,3} of size 96
{3,2,2,2,3} of size 144
{4,2,2,2,3} of size 192
{5,2,2,2,3} of size 240
{6,2,2,2,3} of size 288
{7,2,2,2,3} of size 336
{8,2,2,2,3} of size 384
{9,2,2,2,3} of size 432
{10,2,2,2,3} of size 480
{11,2,2,2,3} of size 528
{12,2,2,2,3} of size 576
{13,2,2,2,3} of size 624
{14,2,2,2,3} of size 672
{15,2,2,2,3} of size 720
{16,2,2,2,3} of size 768
{17,2,2,2,3} of size 816
{18,2,2,2,3} of size 864
{19,2,2,2,3} of size 912
{20,2,2,2,3} of size 960
{21,2,2,2,3} of size 1008
{22,2,2,2,3} of size 1056
{23,2,2,2,3} of size 1104
{24,2,2,2,3} of size 1152
{25,2,2,2,3} of size 1200
{26,2,2,2,3} of size 1248
{27,2,2,2,3} of size 1296
{28,2,2,2,3} of size 1344
{29,2,2,2,3} of size 1392
{30,2,2,2,3} of size 1440
{31,2,2,2,3} of size 1488
{33,2,2,2,3} of size 1584
{34,2,2,2,3} of size 1632
{35,2,2,2,3} of size 1680
{36,2,2,2,3} of size 1728
{37,2,2,2,3} of size 1776
{38,2,2,2,3} of size 1824
{39,2,2,2,3} of size 1872
{40,2,2,2,3} of size 1920
{41,2,2,2,3} of size 1968
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,2,3}*96, {4,2,2,3}*96, {2,2,2,6}*96
3-fold covers : {2,2,2,9}*144, {2,2,6,3}*144, {2,6,2,3}*144, {6,2,2,3}*144
4-fold covers : {4,4,2,3}*192, {2,8,2,3}*192, {8,2,2,3}*192, {2,2,2,12}*192, {2,2,4,6}*192a, {2,4,2,6}*192, {4,2,2,6}*192, {2,2,4,3}*192
5-fold covers : {2,10,2,3}*240, {10,2,2,3}*240, {2,2,2,15}*240
6-fold covers : {2,4,2,9}*288, {4,2,2,9}*288, {2,2,2,18}*288, {2,12,2,3}*288, {12,2,2,3}*288, {4,2,6,3}*288, {4,6,2,3}*288a, {6,4,2,3}*288a, {2,4,6,3}*288, {2,2,6,6}*288a, {2,2,6,6}*288b, {2,6,2,6}*288, {6,2,2,6}*288
7-fold covers : {2,14,2,3}*336, {14,2,2,3}*336, {2,2,2,21}*336
8-fold covers : {4,8,2,3}*384a, {8,4,2,3}*384a, {4,8,2,3}*384b, {8,4,2,3}*384b, {4,4,2,3}*384, {2,16,2,3}*384, {16,2,2,3}*384, {2,2,4,12}*384a, {2,4,2,12}*384, {4,2,2,12}*384, {2,4,4,6}*384, {4,4,2,6}*384, {4,2,4,6}*384a, {2,2,2,24}*384, {2,2,8,6}*384, {2,8,2,6}*384, {8,2,2,6}*384, {2,4,4,3}*384b, {4,2,4,3}*384, {2,2,8,3}*384, {2,2,4,6}*384
9-fold covers : {2,2,2,27}*432, {2,2,6,9}*432, {2,6,2,9}*432, {2,18,2,3}*432, {6,2,2,9}*432, {18,2,2,3}*432, {2,2,6,3}*432, {2,6,6,3}*432a, {2,6,6,3}*432b, {6,2,6,3}*432, {6,6,2,3}*432a, {6,6,2,3}*432b, {6,6,2,3}*432c
10-fold covers : {2,20,2,3}*480, {20,2,2,3}*480, {4,10,2,3}*480, {10,4,2,3}*480, {2,4,2,15}*480, {4,2,2,15}*480, {2,2,10,6}*480, {2,10,2,6}*480, {10,2,2,6}*480, {2,2,2,30}*480
11-fold covers : {2,22,2,3}*528, {22,2,2,3}*528, {2,2,2,33}*528
12-fold covers : {4,4,2,9}*576, {2,8,2,9}*576, {8,2,2,9}*576, {2,2,2,36}*576, {2,2,4,18}*576a, {2,4,2,18}*576, {4,2,2,18}*576, {4,12,2,3}*576a, {12,4,2,3}*576a, {2,24,2,3}*576, {24,2,2,3}*576, {6,8,2,3}*576, {8,2,6,3}*576, {8,6,2,3}*576, {2,8,6,3}*576, {4,4,6,3}*576, {2,2,4,9}*576, {2,2,6,12}*576a, {2,2,6,12}*576b, {2,2,12,6}*576a, {2,6,2,12}*576, {2,12,2,6}*576, {6,2,2,12}*576, {12,2,2,6}*576, {2,4,6,6}*576a, {2,6,4,6}*576, {4,2,6,6}*576a, {4,2,6,6}*576b, {4,6,2,6}*576a, {6,2,4,6}*576a, {6,4,2,6}*576a, {2,2,12,6}*576c, {2,4,6,6}*576c, {2,2,6,3}*576, {2,2,12,3}*576, {2,6,4,3}*576, {4,6,2,3}*576, {6,2,4,3}*576, {6,4,2,3}*576, {6,6,2,3}*576
13-fold covers : {2,26,2,3}*624, {26,2,2,3}*624, {2,2,2,39}*624
14-fold covers : {2,28,2,3}*672, {28,2,2,3}*672, {4,14,2,3}*672, {14,4,2,3}*672, {2,4,2,21}*672, {4,2,2,21}*672, {2,2,14,6}*672, {2,14,2,6}*672, {14,2,2,6}*672, {2,2,2,42}*672
15-fold covers : {2,10,2,9}*720, {10,2,2,9}*720, {2,2,2,45}*720, {2,10,6,3}*720, {6,10,2,3}*720, {10,2,6,3}*720, {10,6,2,3}*720, {2,2,6,15}*720, {2,6,2,15}*720, {2,30,2,3}*720, {6,2,2,15}*720, {30,2,2,3}*720
16-fold covers : {4,8,2,3}*768a, {8,4,2,3}*768a, {8,8,2,3}*768a, {8,8,2,3}*768b, {8,8,2,3}*768c, {8,8,2,3}*768d, {4,16,2,3}*768a, {16,4,2,3}*768a, {4,16,2,3}*768b, {16,4,2,3}*768b, {4,4,2,3}*768, {4,8,2,3}*768b, {8,4,2,3}*768b, {2,32,2,3}*768, {32,2,2,3}*768, {4,4,4,6}*768, {2,4,4,12}*768, {4,4,2,12}*768, {4,2,4,12}*768a, {2,4,8,6}*768a, {2,8,4,6}*768a, {4,8,2,6}*768a, {8,4,2,6}*768a, {2,2,8,12}*768a, {2,2,4,24}*768a, {2,4,8,6}*768b, {2,8,4,6}*768b, {4,8,2,6}*768b, {8,4,2,6}*768b, {2,2,8,12}*768b, {2,2,4,24}*768b, {2,4,4,6}*768a, {4,4,2,6}*768, {2,2,4,12}*768a, {4,2,8,6}*768, {8,2,4,6}*768a, {2,8,2,12}*768, {8,2,2,12}*768, {2,4,2,24}*768, {4,2,2,24}*768, {2,2,16,6}*768, {2,16,2,6}*768, {16,2,2,6}*768, {2,2,2,48}*768, {4,4,4,3}*768b, {2,2,8,3}*768, {2,4,4,3}*768b, {2,4,8,3}*768, {2,8,4,3}*768, {8,2,4,3}*768, {4,2,8,3}*768, {2,2,4,12}*768b, {2,2,4,6}*768b, {2,2,4,12}*768c, {2,4,4,6}*768d, {4,2,4,6}*768, {2,2,8,6}*768b, {2,2,8,6}*768c
17-fold covers : {2,34,2,3}*816, {34,2,2,3}*816, {2,2,2,51}*816
18-fold covers : {2,4,2,27}*864, {4,2,2,27}*864, {2,2,2,54}*864, {2,36,2,3}*864, {36,2,2,3}*864, {2,12,2,9}*864, {12,2,2,9}*864, {2,12,6,3}*864a, {4,2,6,9}*864, {4,6,2,9}*864a, {4,18,2,3}*864a, {6,4,2,9}*864a, {18,4,2,3}*864a, {4,6,6,3}*864a, {4,2,6,3}*864, {2,4,6,9}*864, {2,4,6,3}*864a, {2,2,6,18}*864a, {2,2,6,18}*864b, {2,2,18,6}*864a, {2,6,2,18}*864, {2,18,2,6}*864, {6,2,2,18}*864, {18,2,2,6}*864, {2,2,6,6}*864a, {2,2,6,6}*864b, {2,6,6,6}*864a, {6,12,2,3}*864a, {6,12,2,3}*864b, {12,2,6,3}*864, {12,6,2,3}*864a, {12,6,2,3}*864b, {2,12,6,3}*864b, {6,4,6,3}*864, {6,12,2,3}*864c, {12,6,2,3}*864c, {4,6,6,3}*864d, {2,4,6,3}*864b, {4,4,2,3}*864, {4,6,2,3}*864, {6,4,2,3}*864, {2,2,6,6}*864d, {2,6,6,6}*864b, {2,6,6,6}*864c, {2,6,6,6}*864d, {2,6,6,6}*864g, {6,2,6,6}*864a, {6,2,6,6}*864b, {6,6,2,6}*864a, {6,6,2,6}*864b, {6,6,2,6}*864c
19-fold covers : {2,38,2,3}*912, {38,2,2,3}*912, {2,2,2,57}*912
20-fold covers : {4,20,2,3}*960, {20,4,2,3}*960, {2,40,2,3}*960, {40,2,2,3}*960, {8,10,2,3}*960, {10,8,2,3}*960, {4,4,2,15}*960, {2,8,2,15}*960, {8,2,2,15}*960, {2,2,10,12}*960, {2,10,2,12}*960, {10,2,2,12}*960, {2,2,20,6}*960a, {2,20,2,6}*960, {20,2,2,6}*960, {2,4,10,6}*960, {2,10,4,6}*960, {4,2,10,6}*960, {4,10,2,6}*960, {10,2,4,6}*960a, {10,4,2,6}*960, {2,2,2,60}*960, {2,2,4,30}*960a, {2,4,2,30}*960, {4,2,2,30}*960, {2,10,4,3}*960, {10,2,4,3}*960, {2,2,4,15}*960
21-fold covers : {2,14,2,9}*1008, {14,2,2,9}*1008, {2,2,2,63}*1008, {2,14,6,3}*1008, {6,14,2,3}*1008, {14,2,6,3}*1008, {14,6,2,3}*1008, {2,2,6,21}*1008, {2,6,2,21}*1008, {2,42,2,3}*1008, {6,2,2,21}*1008, {42,2,2,3}*1008
22-fold covers : {2,44,2,3}*1056, {44,2,2,3}*1056, {4,22,2,3}*1056, {22,4,2,3}*1056, {2,4,2,33}*1056, {4,2,2,33}*1056, {2,2,22,6}*1056, {2,22,2,6}*1056, {22,2,2,6}*1056, {2,2,2,66}*1056
23-fold covers : {2,46,2,3}*1104, {46,2,2,3}*1104, {2,2,2,69}*1104
24-fold covers : {4,8,2,9}*1152a, {8,4,2,9}*1152a, {8,4,6,3}*1152a, {8,12,2,3}*1152a, {12,8,2,3}*1152a, {4,8,6,3}*1152a, {4,24,2,3}*1152a, {24,4,2,3}*1152a, {4,8,2,9}*1152b, {8,4,2,9}*1152b, {8,4,6,3}*1152b, {8,12,2,3}*1152b, {12,8,2,3}*1152b, {4,8,6,3}*1152b, {4,24,2,3}*1152b, {24,4,2,3}*1152b, {4,4,2,9}*1152, {4,4,6,3}*1152, {4,12,2,3}*1152a, {12,4,2,3}*1152a, {2,16,2,9}*1152, {16,2,2,9}*1152, {6,16,2,3}*1152, {16,2,6,3}*1152, {16,6,2,3}*1152, {2,16,6,3}*1152, {2,48,2,3}*1152, {48,2,2,3}*1152, {2,4,4,18}*1152, {4,4,2,18}*1152, {2,2,4,36}*1152a, {4,4,6,6}*1152a, {6,4,4,6}*1152, {4,4,6,6}*1152c, {2,4,12,6}*1152a, {2,6,4,12}*1152, {2,12,4,6}*1152, {4,12,2,6}*1152a, {6,2,4,12}*1152a, {12,4,2,6}*1152a, {2,4,12,6}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152b, {4,2,4,18}*1152a, {2,4,2,36}*1152, {4,2,2,36}*1152, {4,6,4,6}*1152a, {4,2,12,6}*1152a, {4,2,6,12}*1152b, {4,2,6,12}*1152c, {4,2,12,6}*1152b, {4,6,2,12}*1152a, {6,4,2,12}*1152a, {12,2,4,6}*1152a, {2,4,6,12}*1152b, {2,4,6,12}*1152c, {2,12,2,12}*1152, {12,2,2,12}*1152, {2,2,8,18}*1152, {2,8,2,18}*1152, {8,2,2,18}*1152, {2,2,2,72}*1152, {2,6,8,6}*1152, {2,8,6,6}*1152a, {6,2,8,6}*1152, {6,8,2,6}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152b, {8,6,2,6}*1152, {2,2,24,6}*1152a, {2,8,6,6}*1152c, {2,2,6,24}*1152b, {2,2,6,24}*1152c, {2,2,24,6}*1152b, {2,6,2,24}*1152, {2,24,2,6}*1152, {6,2,2,24}*1152, {24,2,2,6}*1152, {2,4,4,9}*1152b, {4,2,4,9}*1152, {2,2,8,9}*1152, {2,2,4,18}*1152, {4,12,2,3}*1152b, {12,4,2,3}*1152b, {2,12,4,3}*1152, {12,2,4,3}*1152, {4,6,4,3}*1152a, {6,4,4,3}*1152b, {4,2,6,3}*1152, {4,2,12,3}*1152, {4,6,2,3}*1152b, {4,12,2,3}*1152c, {6,4,2,3}*1152b, {6,12,2,3}*1152a, {12,4,2,3}*1152c, {12,6,2,3}*1152a, {2,2,12,3}*1152, {2,2,24,3}*1152, {2,6,8,3}*1152, {6,2,8,3}*1152, {6,8,2,3}*1152b, {6,12,2,3}*1152b, {8,6,2,3}*1152b, {12,6,2,3}*1152b, {6,6,2,3}*1152b, {6,8,2,3}*1152c, {8,6,2,3}*1152c, {2,4,6,3}*1152a, {2,4,12,3}*1152, {2,2,6,6}*1152a, {2,2,6,12}*1152a, {2,2,12,6}*1152a, {2,2,12,6}*1152b, {2,4,6,6}*1152a, {2,6,4,6}*1152a, {2,6,4,6}*1152b, {2,6,6,6}*1152b, {4,6,2,6}*1152, {6,2,4,6}*1152, {6,4,2,6}*1152, {6,6,2,6}*1152
25-fold covers : {2,50,2,3}*1200, {50,2,2,3}*1200, {2,2,2,75}*1200, {2,2,10,3}*1200, {10,10,2,3}*1200a, {10,10,2,3}*1200b, {10,10,2,3}*1200c, {2,2,10,15}*1200, {2,10,2,15}*1200, {10,2,2,15}*1200
26-fold covers : {2,52,2,3}*1248, {52,2,2,3}*1248, {4,26,2,3}*1248, {26,4,2,3}*1248, {2,4,2,39}*1248, {4,2,2,39}*1248, {2,2,26,6}*1248, {2,26,2,6}*1248, {26,2,2,6}*1248, {2,2,2,78}*1248
27-fold covers : {2,2,2,81}*1296, {2,2,18,9}*1296, {2,18,2,9}*1296, {18,2,2,9}*1296, {2,2,6,9}*1296a, {2,6,6,9}*1296a, {2,18,6,3}*1296a, {2,2,6,27}*1296, {2,6,2,27}*1296, {2,54,2,3}*1296, {6,2,2,27}*1296, {54,2,2,3}*1296, {2,2,6,9}*1296b, {2,2,6,9}*1296c, {2,6,6,3}*1296a, {2,6,6,3}*1296b, {2,2,6,9}*1296d, {2,2,6,3}*1296, {2,2,18,3}*1296, {2,6,6,9}*1296b, {2,18,6,3}*1296b, {6,2,6,9}*1296, {6,6,2,9}*1296a, {6,6,2,9}*1296b, {6,6,2,9}*1296c, {6,18,2,3}*1296a, {6,18,2,3}*1296b, {18,2,6,3}*1296, {18,6,2,3}*1296a, {18,6,2,3}*1296b, {6,6,6,3}*1296a, {2,6,6,3}*1296c, {6,6,6,3}*1296b, {2,6,6,3}*1296d, {2,6,6,3}*1296e, {6,2,6,3}*1296, {6,6,2,3}*1296a, {6,6,2,3}*1296b, {6,6,2,3}*1296c, {6,6,6,3}*1296c, {6,6,6,3}*1296d, {6,6,2,3}*1296d, {6,6,6,3}*1296e
28-fold covers : {4,28,2,3}*1344, {28,4,2,3}*1344, {2,56,2,3}*1344, {56,2,2,3}*1344, {8,14,2,3}*1344, {14,8,2,3}*1344, {4,4,2,21}*1344, {2,8,2,21}*1344, {8,2,2,21}*1344, {2,2,14,12}*1344, {2,14,2,12}*1344, {14,2,2,12}*1344, {2,2,28,6}*1344a, {2,28,2,6}*1344, {28,2,2,6}*1344, {2,4,14,6}*1344, {2,14,4,6}*1344, {4,2,14,6}*1344, {4,14,2,6}*1344, {14,2,4,6}*1344a, {14,4,2,6}*1344, {2,2,2,84}*1344, {2,2,4,42}*1344a, {2,4,2,42}*1344, {4,2,2,42}*1344, {2,14,4,3}*1344, {14,2,4,3}*1344, {2,2,4,21}*1344
29-fold covers : {2,58,2,3}*1392, {58,2,2,3}*1392, {2,2,2,87}*1392
30-fold covers : {2,20,2,9}*1440, {20,2,2,9}*1440, {4,10,2,9}*1440, {10,4,2,9}*1440, {2,4,2,45}*1440, {4,2,2,45}*1440, {2,2,10,18}*1440, {2,10,2,18}*1440, {10,2,2,18}*1440, {2,2,2,90}*1440, {10,12,2,3}*1440, {12,10,2,3}*1440, {6,20,2,3}*1440a, {20,2,6,3}*1440, {20,6,2,3}*1440a, {2,20,6,3}*1440, {10,4,6,3}*1440, {4,10,6,3}*1440, {2,12,2,15}*1440, {12,2,2,15}*1440, {2,60,2,3}*1440, {60,2,2,3}*1440, {4,2,6,15}*1440, {4,6,2,15}*1440a, {4,30,2,3}*1440a, {6,4,2,15}*1440a, {30,4,2,3}*1440a, {2,4,6,15}*1440, {2,2,30,6}*1440a, {2,6,10,6}*1440, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {6,2,10,6}*1440, {6,10,2,6}*1440, {10,2,6,6}*1440a, {10,2,6,6}*1440b, {10,6,2,6}*1440, {2,2,6,30}*1440b, {2,2,6,30}*1440c, {2,2,30,6}*1440b, {2,6,2,30}*1440, {2,30,2,6}*1440, {6,2,2,30}*1440, {30,2,2,6}*1440
31-fold covers : {2,62,2,3}*1488, {62,2,2,3}*1488, {2,2,2,93}*1488
33-fold covers : {2,22,2,9}*1584, {22,2,2,9}*1584, {2,2,2,99}*1584, {2,22,6,3}*1584, {6,22,2,3}*1584, {22,2,6,3}*1584, {22,6,2,3}*1584, {2,2,6,33}*1584, {2,6,2,33}*1584, {2,66,2,3}*1584, {6,2,2,33}*1584, {66,2,2,3}*1584
34-fold covers : {2,68,2,3}*1632, {68,2,2,3}*1632, {4,34,2,3}*1632, {34,4,2,3}*1632, {2,4,2,51}*1632, {4,2,2,51}*1632, {2,2,34,6}*1632, {2,34,2,6}*1632, {34,2,2,6}*1632, {2,2,2,102}*1632
35-fold covers : {10,14,2,3}*1680, {14,10,2,3}*1680, {2,14,2,15}*1680, {14,2,2,15}*1680, {2,10,2,21}*1680, {10,2,2,21}*1680, {2,70,2,3}*1680, {70,2,2,3}*1680, {2,2,2,105}*1680
36-fold covers : {4,4,2,27}*1728, {2,8,2,27}*1728, {8,2,2,27}*1728, {2,2,2,108}*1728, {2,2,4,54}*1728a, {2,4,2,54}*1728, {4,2,2,54}*1728, {4,12,2,9}*1728a, {12,4,2,9}*1728a, {4,36,2,3}*1728a, {36,4,2,3}*1728a, {4,12,6,3}*1728a, {2,72,2,3}*1728, {72,2,2,3}*1728, {2,24,2,9}*1728, {24,2,2,9}*1728, {2,24,6,3}*1728a, {6,8,2,9}*1728, {8,2,6,9}*1728, {8,6,2,9}*1728, {8,18,2,3}*1728, {18,8,2,3}*1728, {8,6,6,3}*1728a, {8,2,6,3}*1728, {2,8,6,9}*1728, {4,4,6,9}*1728, {2,8,6,3}*1728a, {4,4,6,3}*1728a, {2,2,4,27}*1728, {2,2,12,18}*1728a, {2,2,18,12}*1728a, {2,12,2,18}*1728, {2,18,2,12}*1728, {12,2,2,18}*1728, {18,2,2,12}*1728, {2,2,6,36}*1728a, {2,2,6,36}*1728b, {2,2,36,6}*1728a, {2,6,2,36}*1728, {2,36,2,6}*1728, {6,2,2,36}*1728, {36,2,2,6}*1728, {2,2,6,12}*1728a, {2,2,6,12}*1728b, {2,2,12,6}*1728b, {2,6,6,12}*1728a, {2,12,6,6}*1728a, {2,4,6,18}*1728a, {2,4,18,6}*1728a, {2,6,4,18}*1728, {2,18,4,6}*1728, {4,2,6,18}*1728a, {4,2,6,18}*1728b, {4,2,18,6}*1728a, {4,6,2,18}*1728a, {4,18,2,6}*1728a, {6,2,4,18}*1728a, {6,4,2,18}*1728a, {18,2,4,6}*1728a, {18,4,2,6}*1728a, {4,6,6,6}*1728a, {2,4,6,6}*1728b, {2,6,12,6}*1728a, {4,2,6,6}*1728a, {4,2,6,6}*1728b, {2,2,12,18}*1728b, {2,4,6,18}*1728b, {2,2,12,6}*1728c, {2,4,6,6}*1728c, {6,24,2,3}*1728a, {6,24,2,3}*1728b, {24,2,6,3}*1728, {24,6,2,3}*1728a, {24,6,2,3}*1728b, {2,24,6,3}*1728b, {12,12,2,3}*1728a, {12,12,2,3}*1728b, {12,12,2,3}*1728c, {12,4,6,3}*1728, {6,8,6,3}*1728, {6,24,2,3}*1728c, {24,6,2,3}*1728c, {8,6,6,3}*1728b, {4,12,6,3}*1728d, {2,2,6,9}*1728, {2,18,4,3}*1728, {4,6,2,9}*1728, {6,4,2,9}*1728, {6,6,2,9}*1728, {18,2,4,3}*1728, {2,2,12,9}*1728, {2,6,4,9}*1728, {4,18,2,3}*1728, {6,2,4,9}*1728, {18,4,2,3}*1728, {4,6,6,3}*1728a, {2,2,6,3}*1728, {2,2,12,3}*1728, {2,6,12,3}*1728a, {6,8,2,3}*1728, {8,6,2,3}*1728, {2,8,6,3}*1728b, {4,4,6,3}*1728b, {4,4,2,3}*1728, {4,12,2,3}*1728, {12,4,2,3}*1728, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {2,6,6,12}*1728d, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {2,12,6,6}*1728b, {2,12,6,6}*1728d, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,2,12,6}*1728a, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {6,6,2,12}*1728c, {6,12,2,6}*1728a, {6,12,2,6}*1728b, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {4,6,6,6}*1728d, {4,6,6,6}*1728f, {6,4,6,6}*1728a, {6,6,4,6}*1728a, {6,6,4,6}*1728b, {4,2,6,6}*1728d, {2,2,6,12}*1728g, {2,2,12,6}*1728g, {2,6,6,12}*1728e, {2,12,6,6}*1728e, {4,6,6,6}*1728g, {6,4,6,6}*1728c, {6,6,4,6}*1728c, {2,4,6,6}*1728h, {2,6,12,6}*1728f, {2,6,12,6}*1728g, {2,12,6,6}*1728f, {6,2,12,6}*1728c, {6,12,2,6}*1728c, {12,6,2,6}*1728c, {4,6,6,6}*1728i, {4,6,6,3}*1728b, {6,4,6,3}*1728b, {6,6,4,3}*1728a, {6,6,4,3}*1728b, {6,6,4,3}*1728c, {6,6,6,3}*1728d, {2,6,6,3}*1728, {2,6,12,3}*1728b, {6,2,6,3}*1728, {6,2,12,3}*1728, {6,6,2,3}*1728a, {6,6,2,3}*1728b, {6,12,2,3}*1728a, {6,12,2,3}*1728b, {12,6,2,3}*1728a, {12,6,2,3}*1728b, {2,2,4,6}*1728b, {2,2,4,12}*1728b, {2,4,4,6}*1728b, {2,4,6,6}*1728j, {2,4,6,6}*1728k, {2,6,4,6}*1728b, {4,4,2,6}*1728, {4,6,2,6}*1728, {6,4,2,6}*1728, {2,2,6,12}*1728i
37-fold covers : {2,74,2,3}*1776, {74,2,2,3}*1776, {2,2,2,111}*1776
38-fold covers : {2,76,2,3}*1824, {76,2,2,3}*1824, {4,38,2,3}*1824, {38,4,2,3}*1824, {2,4,2,57}*1824, {4,2,2,57}*1824, {2,2,38,6}*1824, {2,38,2,6}*1824, {38,2,2,6}*1824, {2,2,2,114}*1824
39-fold covers : {2,26,2,9}*1872, {26,2,2,9}*1872, {2,2,2,117}*1872, {2,26,6,3}*1872, {6,26,2,3}*1872, {26,2,6,3}*1872, {26,6,2,3}*1872, {2,2,6,39}*1872, {2,6,2,39}*1872, {2,78,2,3}*1872, {6,2,2,39}*1872, {78,2,2,3}*1872
40-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,20,2,3}*1920a, {20,8,2,3}*1920a, {4,40,2,3}*1920a, {40,4,2,3}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,20,2,3}*1920b, {20,8,2,3}*1920b, {4,40,2,3}*1920b, {40,4,2,3}*1920b, {4,4,2,15}*1920, {4,20,2,3}*1920, {20,4,2,3}*1920, {2,16,2,15}*1920, {16,2,2,15}*1920, {10,16,2,3}*1920, {16,10,2,3}*1920, {2,80,2,3}*1920, {80,2,2,3}*1920, {2,4,4,30}*1920, {4,4,2,30}*1920, {2,2,4,60}*1920a, {4,4,10,6}*1920, {10,4,4,6}*1920, {2,10,4,12}*1920, {10,2,4,12}*1920a, {2,4,20,6}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920, {2,2,20,12}*1920, {4,2,4,30}*1920a, {2,4,2,60}*1920, {4,2,2,60}*1920, {4,10,4,6}*1920, {4,2,10,12}*1920, {4,10,2,12}*1920, {10,4,2,12}*1920, {4,2,20,6}*1920a, {20,2,4,6}*1920a, {2,4,10,12}*1920, {2,20,2,12}*1920, {20,2,2,12}*1920, {2,2,8,30}*1920, {2,8,2,30}*1920, {8,2,2,30}*1920, {2,2,2,120}*1920, {2,8,10,6}*1920, {2,10,8,6}*1920, {8,2,10,6}*1920, {8,10,2,6}*1920, {10,2,8,6}*1920, {10,8,2,6}*1920, {2,2,10,24}*1920, {2,10,2,24}*1920, {10,2,2,24}*1920, {2,2,40,6}*1920, {2,40,2,6}*1920, {40,2,2,6}*1920, {2,20,4,3}*1920, {20,2,4,3}*1920, {4,10,4,3}*1920, {10,4,4,3}*1920b, {2,10,8,3}*1920, {10,2,8,3}*1920, {2,4,4,15}*1920b, {4,2,4,15}*1920, {2,2,8,15}*1920, {2,2,20,6}*1920a, {2,10,4,6}*1920, {10,2,4,6}*1920, {2,2,4,30}*1920
41-fold covers : {2,82,2,3}*1968, {82,2,2,3}*1968, {2,2,2,123}*1968
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (8,9);;
s4 := (7,8);;
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 ];;
poly := F / rels;;

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

```

to this polytope