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# Polytope of Type {2,12,6}

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

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

```

to this polytope