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# Polytope of Type {24,6}

Atlas Canonical Name : {24,6}*576c
if this polytope has a name.
Group : SmallGroup(576,8328)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 48, 144, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,6,2} of size 1152
Vertex Figure Of :
{2,24,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6}*288a
3-fold quotients : {8,6}*192c
4-fold quotients : {12,6}*144d
6-fold quotients : {4,6}*96
8-fold quotients : {6,6}*72a
12-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
24-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
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}*1152i, {24,6}*1152d, {24,12}*1152u
3-fold covers : {72,6}*1728b, {24,18}*1728c, {24,6}*1728c, {24,6}*1728g
Permutation Representation (GAP) :
```s0 := (  1, 77)(  2, 78)(  3, 80)(  4, 79)(  5, 74)(  6, 73)(  7, 75)(  8, 76)
(  9, 93)( 10, 94)( 11, 96)( 12, 95)( 13, 90)( 14, 89)( 15, 91)( 16, 92)
( 17, 85)( 18, 86)( 19, 88)( 20, 87)( 21, 82)( 22, 81)( 23, 83)( 24, 84)
( 25,101)( 26,102)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31, 99)( 32,100)
( 33,117)( 34,118)( 35,120)( 36,119)( 37,114)( 38,113)( 39,115)( 40,116)
( 41,109)( 42,110)( 43,112)( 44,111)( 45,106)( 46,105)( 47,107)( 48,108)
( 49,125)( 50,126)( 51,128)( 52,127)( 53,122)( 54,121)( 55,123)( 56,124)
( 57,141)( 58,142)( 59,144)( 60,143)( 61,138)( 62,137)( 63,139)( 64,140)
( 65,133)( 66,134)( 67,136)( 68,135)( 69,130)( 70,129)( 71,131)( 72,132);;
s1 := (  1,  9)(  2, 10)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 16)(  8, 15)
( 19, 22)( 20, 21)( 23, 24)( 25, 57)( 26, 58)( 27, 62)( 28, 61)( 29, 60)
( 30, 59)( 31, 64)( 32, 63)( 33, 49)( 34, 50)( 35, 54)( 36, 53)( 37, 52)
( 38, 51)( 39, 56)( 40, 55)( 41, 65)( 42, 66)( 43, 70)( 44, 69)( 45, 68)
( 46, 67)( 47, 72)( 48, 71)( 73, 81)( 74, 82)( 75, 86)( 76, 85)( 77, 84)
( 78, 83)( 79, 88)( 80, 87)( 91, 94)( 92, 93)( 95, 96)( 97,129)( 98,130)
( 99,134)(100,133)(101,132)(102,131)(103,136)(104,135)(105,121)(106,122)
(107,126)(108,125)(109,124)(110,123)(111,128)(112,127)(113,137)(114,138)
(115,142)(116,141)(117,140)(118,139)(119,144)(120,143);;
s2 := (  1, 49)(  2, 50)(  3, 55)(  4, 56)(  5, 54)(  6, 53)(  7, 51)(  8, 52)
(  9, 57)( 10, 58)( 11, 63)( 12, 64)( 13, 62)( 14, 61)( 15, 59)( 16, 60)
( 17, 65)( 18, 66)( 19, 71)( 20, 72)( 21, 70)( 22, 69)( 23, 67)( 24, 68)
( 27, 31)( 28, 32)( 29, 30)( 35, 39)( 36, 40)( 37, 38)( 43, 47)( 44, 48)
( 45, 46)( 73,122)( 74,121)( 75,128)( 76,127)( 77,125)( 78,126)( 79,124)
( 80,123)( 81,130)( 82,129)( 83,136)( 84,135)( 85,133)( 86,134)( 87,132)
( 88,131)( 89,138)( 90,137)( 91,144)( 92,143)( 93,141)( 94,142)( 95,140)
( 96,139)( 97, 98)( 99,104)(100,103)(105,106)(107,112)(108,111)(113,114)
(115,120)(116,119);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope