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# Polytope of Type {24,12}

Atlas Canonical Name : {24,12}*576a
if this polytope has a name.
Group : SmallGroup(576,2279)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 24, 144, 12
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
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 : {12,12}*288b
3-fold quotients : {8,12}*192b
4-fold quotients : {6,12}*144b, {12,6}*144c
6-fold quotients : {4,12}*96a
8-fold quotients : {6,6}*72b
9-fold quotients : {8,4}*64b
12-fold quotients : {2,12}*48, {4,6}*48a
16-fold quotients : {6,3}*36
18-fold quotients : {4,4}*32
24-fold quotients : {2,6}*24
36-fold quotients : {2,4}*16, {4,2}*16
48-fold quotients : {2,3}*12
72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,12}*1152c, {24,24}*1152a, {24,24}*1152j
3-fold covers : {24,36}*1728a, {24,12}*1728a, {24,12}*1728p
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)
( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 38, 39)
( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 55, 64)( 56, 66)( 57, 65)
( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 91)( 74, 93)
( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 97)( 80, 99)( 81, 98)( 82,100)
( 83,102)( 84,101)( 85,103)( 86,105)( 87,104)( 88,106)( 89,108)( 90,107)
(109,127)(110,129)(111,128)(112,130)(113,132)(114,131)(115,133)(116,135)
(117,134)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)
(125,144)(126,143);;
s1 := (  1, 74)(  2, 73)(  3, 75)(  4, 80)(  5, 79)(  6, 81)(  7, 77)(  8, 76)
(  9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19,101)( 20,100)( 21,102)( 22,107)( 23,106)( 24,108)
( 25,104)( 26,103)( 27,105)( 28, 92)( 29, 91)( 30, 93)( 31, 98)( 32, 97)
( 33, 99)( 34, 95)( 35, 94)( 36, 96)( 37,119)( 38,118)( 39,120)( 40,125)
( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)( 48,111)
( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,128)( 56,127)
( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)
( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141);;
s2 := (  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)
( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 34)( 26, 36)
( 27, 35)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 52)
( 44, 54)( 45, 53)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)
( 66, 68)( 71, 72)( 73,130)( 74,132)( 75,131)( 76,127)( 77,129)( 78,128)
( 79,133)( 80,135)( 81,134)( 82,139)( 83,141)( 84,140)( 85,136)( 86,138)
( 87,137)( 88,142)( 89,144)( 90,143)( 91,112)( 92,114)( 93,113)( 94,109)
( 95,111)( 96,110)( 97,115)( 98,117)( 99,116)(100,121)(101,123)(102,122)
(103,118)(104,120)(105,119)(106,124)(107,126)(108,125);;
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope