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# Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 48, 144, 24, 2
Order of s0s1s2s3 : 12
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 : {12,6,2}*576a
3-fold quotients : {4,6,2}*384b
4-fold quotients : {12,6,2}*288a, {12,6,2}*288d
6-fold quotients : {4,6,2}*192
8-fold quotients : {6,6,2}*144a
12-fold quotients : {12,2,2}*96, {4,6,2}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {4,3,2}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {4,2,2}*32
48-fold quotients : {2,3,2}*24, {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1,  3)(  2,  4)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 13, 15)( 14, 16)
( 17, 23)( 18, 24)( 19, 21)( 20, 22)( 25, 27)( 26, 28)( 29, 35)( 30, 36)
( 31, 33)( 32, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 49, 51)( 50, 52)( 53, 59)( 54, 60)( 55, 57)( 56, 58)( 61, 63)( 62, 64)
( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 73,111)( 74,112)( 75,109)( 76,110)
( 77,119)( 78,120)( 79,117)( 80,118)( 81,115)( 82,116)( 83,113)( 84,114)
( 85,123)( 86,124)( 87,121)( 88,122)( 89,131)( 90,132)( 91,129)( 92,130)
( 93,127)( 94,128)( 95,125)( 96,126)( 97,135)( 98,136)( 99,133)(100,134)
(101,143)(102,144)(103,141)(104,142)(105,139)(106,140)(107,137)(108,138);;
s1 := (  1, 77)(  2, 79)(  3, 78)(  4, 80)(  5, 73)(  6, 75)(  7, 74)(  8, 76)
(  9, 81)( 10, 83)( 11, 82)( 12, 84)( 13,101)( 14,103)( 15,102)( 16,104)
( 17, 97)( 18, 99)( 19, 98)( 20,100)( 21,105)( 22,107)( 23,106)( 24,108)
( 25, 89)( 26, 91)( 27, 90)( 28, 92)( 29, 85)( 30, 87)( 31, 86)( 32, 88)
( 33, 93)( 34, 95)( 35, 94)( 36, 96)( 37,113)( 38,115)( 39,114)( 40,116)
( 41,109)( 42,111)( 43,110)( 44,112)( 45,117)( 46,119)( 47,118)( 48,120)
( 49,137)( 50,139)( 51,138)( 52,140)( 53,133)( 54,135)( 55,134)( 56,136)
( 57,141)( 58,143)( 59,142)( 60,144)( 61,125)( 62,127)( 63,126)( 64,128)
( 65,121)( 66,123)( 67,122)( 68,124)( 69,129)( 70,131)( 71,130)( 72,132);;
s2 := (  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 29)(  6, 32)(  7, 31)(  8, 30)
(  9, 33)( 10, 36)( 11, 35)( 12, 34)( 14, 16)( 18, 20)( 22, 24)( 37, 61)
( 38, 64)( 39, 63)( 40, 62)( 41, 65)( 42, 68)( 43, 67)( 44, 66)( 45, 69)
( 46, 72)( 47, 71)( 48, 70)( 50, 52)( 54, 56)( 58, 60)( 73, 97)( 74,100)
( 75, 99)( 76, 98)( 77,101)( 78,104)( 79,103)( 80,102)( 81,105)( 82,108)
( 83,107)( 84,106)( 86, 88)( 90, 92)( 94, 96)(109,133)(110,136)(111,135)
(112,134)(113,137)(114,140)(115,139)(116,138)(117,141)(118,144)(119,143)
(120,142)(122,124)(126,128)(130,132);;
s3 := (145,146);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope