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Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32554)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 144, 288, 24
Order of s0s1s2 : 4
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*576
   4-fold quotients : {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {8,4}*128b
   16-fold quotients : {6,4}*72
   18-fold quotients : {4,4}*64
   36-fold quotients : {4,4}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   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,  4)(  3,  9)(  5,  8)( 10, 13)( 12, 18)( 14, 17)( 19, 31)( 20, 29)
( 21, 36)( 22, 28)( 23, 35)( 24, 33)( 25, 34)( 26, 32)( 27, 30)( 37, 49)
( 38, 47)( 39, 54)( 40, 46)( 41, 53)( 42, 51)( 43, 52)( 44, 50)( 45, 48)
( 55, 58)( 57, 63)( 59, 62)( 64, 67)( 66, 72)( 68, 71)( 73,139)( 74,137)
( 75,144)( 76,136)( 77,143)( 78,141)( 79,142)( 80,140)( 81,138)( 82,130)
( 83,128)( 84,135)( 85,127)( 86,134)( 87,132)( 88,133)( 89,131)( 90,129)
( 91,112)( 92,110)( 93,117)( 94,109)( 95,116)( 96,114)( 97,115)( 98,113)
( 99,111)(100,121)(101,119)(102,126)(103,118)(104,125)(105,123)(106,124)
(107,122)(108,120);;
s2 := (  4,  9)(  5,  7)(  6,  8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)
( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 37, 64)( 38, 65)( 39, 66)( 40, 72)
( 41, 70)( 42, 71)( 43, 68)( 44, 69)( 45, 67)( 46, 55)( 47, 56)( 48, 57)
( 49, 63)( 50, 61)( 51, 62)( 52, 59)( 53, 60)( 54, 58)( 76, 81)( 77, 79)
( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)(103,108)
(104,106)(105,107)(109,136)(110,137)(111,138)(112,144)(113,142)(114,143)
(115,140)(116,141)(117,139)(118,127)(119,128)(120,129)(121,135)(122,133)
(123,134)(124,131)(125,132)(126,130);;
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, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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)!(  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,  4)(  3,  9)(  5,  8)( 10, 13)( 12, 18)( 14, 17)( 19, 31)
( 20, 29)( 21, 36)( 22, 28)( 23, 35)( 24, 33)( 25, 34)( 26, 32)( 27, 30)
( 37, 49)( 38, 47)( 39, 54)( 40, 46)( 41, 53)( 42, 51)( 43, 52)( 44, 50)
( 45, 48)( 55, 58)( 57, 63)( 59, 62)( 64, 67)( 66, 72)( 68, 71)( 73,139)
( 74,137)( 75,144)( 76,136)( 77,143)( 78,141)( 79,142)( 80,140)( 81,138)
( 82,130)( 83,128)( 84,135)( 85,127)( 86,134)( 87,132)( 88,133)( 89,131)
( 90,129)( 91,112)( 92,110)( 93,117)( 94,109)( 95,116)( 96,114)( 97,115)
( 98,113)( 99,111)(100,121)(101,119)(102,126)(103,118)(104,125)(105,123)
(106,124)(107,122)(108,120);
s2 := Sym(144)!(  4,  9)(  5,  7)(  6,  8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)
( 23, 25)( 24, 26)( 31, 36)( 32, 34)( 33, 35)( 37, 64)( 38, 65)( 39, 66)
( 40, 72)( 41, 70)( 42, 71)( 43, 68)( 44, 69)( 45, 67)( 46, 55)( 47, 56)
( 48, 57)( 49, 63)( 50, 61)( 51, 62)( 52, 59)( 53, 60)( 54, 58)( 76, 81)
( 77, 79)( 78, 80)( 85, 90)( 86, 88)( 87, 89)( 94, 99)( 95, 97)( 96, 98)
(103,108)(104,106)(105,107)(109,136)(110,137)(111,138)(112,144)(113,142)
(114,143)(115,140)(116,141)(117,139)(118,127)(119,128)(120,129)(121,135)
(122,133)(123,134)(124,131)(125,132)(126,130);
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, 
s2*s0*s1*s2*s0*s1*s2*s0*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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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