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Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152f
if this polytope has a name.
Group : SmallGroup(1152,32550)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*576c
   3-fold quotients : {24,4}*384b
   4-fold quotients : {12,12}*288c
   6-fold quotients : {12,4}*192a
   8-fold quotients : {12,6}*144b, {6,12}*144c
   9-fold quotients : {8,4}*128b
   12-fold quotients : {12,4}*96a
   16-fold quotients : {6,6}*72c
   18-fold quotients : {4,4}*64
   24-fold quotients : {12,2}*48, {6,4}*48a
   32-fold quotients : {3,6}*36
   36-fold quotients : {4,4}*32
   48-fold quotients : {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)(  8, 78)
(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)
( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)
( 33,107)( 34,103)( 35,105)( 36,104)( 37,136)( 38,138)( 39,137)( 40,142)
( 41,144)( 42,143)( 43,139)( 44,141)( 45,140)( 46,127)( 47,129)( 48,128)
( 49,133)( 50,135)( 51,134)( 52,130)( 53,132)( 54,131)( 55,118)( 56,120)
( 57,119)( 58,124)( 59,126)( 60,125)( 61,121)( 62,123)( 63,122)( 64,109)
( 65,111)( 66,110)( 67,115)( 68,117)( 69,116)( 70,112)( 71,114)( 72,113);;
s1 := (  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)( 50, 52)
( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)( 61, 68)
( 62, 67)( 63, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)( 78,117)
( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)( 86,124)
( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)( 94,143)
( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)(102,129)
(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);;
s2 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 64)( 38, 69)( 39, 71)( 40, 67)
( 41, 72)( 42, 65)( 43, 70)( 44, 66)( 45, 68)( 46, 55)( 47, 60)( 48, 62)
( 49, 58)( 50, 63)( 51, 56)( 52, 61)( 53, 57)( 54, 59)( 74, 78)( 75, 80)
( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)
(102,107)(104,108)(109,136)(110,141)(111,143)(112,139)(113,144)(114,137)
(115,142)(116,138)(117,140)(118,127)(119,132)(120,134)(121,130)(122,135)
(123,128)(124,133)(125,129)(126,131);;
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*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(144)!(  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)
(  8, 78)(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)
( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)
( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,136)( 38,138)( 39,137)
( 40,142)( 41,144)( 42,143)( 43,139)( 44,141)( 45,140)( 46,127)( 47,129)
( 48,128)( 49,133)( 50,135)( 51,134)( 52,130)( 53,132)( 54,131)( 55,118)
( 56,120)( 57,119)( 58,124)( 59,126)( 60,125)( 61,121)( 62,123)( 63,122)
( 64,109)( 65,111)( 66,110)( 67,115)( 68,117)( 69,116)( 70,112)( 71,114)
( 72,113);
s1 := Sym(144)!(  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)
( 50, 52)( 51, 54)( 55, 65)( 56, 64)( 57, 66)( 58, 71)( 59, 70)( 60, 72)
( 61, 68)( 62, 67)( 63, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)
( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)
( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)
( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)
(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132);
s2 := Sym(144)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 64)( 38, 69)( 39, 71)
( 40, 67)( 41, 72)( 42, 65)( 43, 70)( 44, 66)( 45, 68)( 46, 55)( 47, 60)
( 48, 62)( 49, 58)( 50, 63)( 51, 56)( 52, 61)( 53, 57)( 54, 59)( 74, 78)
( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)
(101,105)(102,107)(104,108)(109,136)(110,141)(111,143)(112,139)(113,144)
(114,137)(115,142)(116,138)(117,140)(118,127)(119,132)(120,134)(121,130)
(122,135)(123,128)(124,133)(125,129)(126,131);
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*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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