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# Polytope of Type {2,12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,97547)
Rank : 4
Schlafli Type : {2,12,24}
Number of vertices, edges, etc : 2, 12, 144, 24
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,24}*576b, {2,12,12}*576b
3-fold quotients : {2,4,24}*384a
4-fold quotients : {2,6,12}*288b, {2,12,6}*288c
6-fold quotients : {2,4,12}*192a, {2,2,24}*192
8-fold quotients : {2,6,6}*144b
9-fold quotients : {2,4,8}*128a
12-fold quotients : {2,2,12}*96, {2,4,6}*96a
16-fold quotients : {2,6,3}*72
18-fold quotients : {2,4,4}*64, {2,2,8}*64
24-fold quotients : {2,2,6}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {2,2,3}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)
( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)
( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)
(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)
(125,142)(126,144)(127,146)(128,145);;
s2 := (  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)
( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)
( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)
( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)( 42,127)
( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)
( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)( 58,138)
( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)( 66,130)
( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)( 74,134);;
s3 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)
( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)( 46, 56)
( 47, 55)( 57, 69)( 58, 71)( 59, 70)( 60, 66)( 61, 68)( 62, 67)( 63, 72)
( 64, 74)( 65, 73)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)
( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)( 88,140)
( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)( 96,111)
( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)(104,124)
(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)
( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)
( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)
(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)
(124,143)(125,142)(126,144)(127,146)(128,145);
s2 := Sym(146)!(  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)
( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)
( 26,101)( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)
( 34,108)( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)
( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)
( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)
( 58,138)( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)
( 66,130)( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)
( 74,134);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)
( 37, 38)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)
( 46, 56)( 47, 55)( 57, 69)( 58, 71)( 59, 70)( 60, 66)( 61, 68)( 62, 67)
( 63, 72)( 64, 74)( 65, 73)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)
( 80,130)( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)
( 88,140)( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)
( 96,111)( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)
(104,124)(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);
poly := sub<Sym(146)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope