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# Polytope of Type {24,12}

Atlas Canonical Name : {24,12}*576c
Also Known As : {24,12|2}. if this polytope has another name.
Group : SmallGroup(576,2829)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 24, 144, 12
Order of s0s1s2 : 24
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,12,2} of size 1152
Vertex Figure Of :
{2,24,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,6}*288a, {12,12}*288a
3-fold quotients : {24,4}*192a, {8,12}*192a
4-fold quotients : {6,12}*144a, {12,6}*144a
6-fold quotients : {4,12}*96a, {12,4}*96a, {24,2}*96, {8,6}*96
8-fold quotients : {6,6}*72a
9-fold quotients : {8,4}*64a
12-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
18-fold quotients : {4,4}*32, {8,2}*32
24-fold quotients : {2,6}*24, {6,2}*24
36-fold quotients : {2,4}*16, {4,2}*16
48-fold quotients : {2,3}*12, {3,2}*12
72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,12}*1152b, {24,24}*1152b, {24,24}*1152g, {48,12}*1152b, {48,12}*1152e
3-fold covers : {72,12}*1728a, {24,36}*1728c, {24,12}*1728d, {24,12}*1728o
Permutation Representation (GAP) :
```s0 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 37, 46)( 38, 47)( 39, 48)( 40, 52)
( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)( 55, 64)( 56, 65)( 57, 66)
( 58, 70)( 59, 71)( 60, 72)( 61, 67)( 62, 68)( 63, 69)( 73,109)( 74,110)
( 75,111)( 76,115)( 77,116)( 78,117)( 79,112)( 80,113)( 81,114)( 82,118)
( 83,119)( 84,120)( 85,124)( 86,125)( 87,126)( 88,121)( 89,122)( 90,123)
( 91,127)( 92,128)( 93,129)( 94,133)( 95,134)( 96,135)( 97,130)( 98,131)
( 99,132)(100,136)(101,137)(102,138)(103,142)(104,143)(105,144)(106,139)
(107,140)(108,141);;
s1 := (  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 79)(  8, 81)
(  9, 80)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 88)
( 17, 90)( 18, 89)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)
( 25, 97)( 26, 99)( 27, 98)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)
( 33,101)( 34,106)( 35,108)( 36,107)( 37,121)( 38,123)( 39,122)( 40,118)
( 41,120)( 42,119)( 43,124)( 44,126)( 45,125)( 46,112)( 47,114)( 48,113)
( 49,109)( 50,111)( 51,110)( 52,115)( 53,117)( 54,116)( 55,139)( 56,141)
( 57,140)( 58,136)( 59,138)( 60,137)( 61,142)( 62,144)( 63,143)( 64,130)
( 65,132)( 66,131)( 67,127)( 68,129)( 69,128)( 70,133)( 71,135)( 72,134);;
s2 := (  1,  2)(  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, 92)( 74, 91)( 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)(109,128)(110,127)(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);;
poly := Group([s0,s1,s2]);;

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

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

```
References : None.
to this polytope