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

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

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

```

to this polytope