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Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32552)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 72, 288, 48
Order of s0s1s2 : 4
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 : {12,4}*576
   4-fold quotients : {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {4,8}*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 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)
( 45, 68)( 46, 55)( 47, 57)( 48, 56)( 49, 61)( 50, 63)( 51, 62)( 52, 58)
( 53, 60)( 54, 59)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)
( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)
(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)
(115,139)(116,141)(117,140)(118,127)(119,129)(120,128)(121,133)(122,135)
(123,134)(124,130)(125,132)(126,131);;
s1 := (  1, 40)(  2, 38)(  3, 45)(  4, 37)(  5, 44)(  6, 42)(  7, 43)(  8, 41)
(  9, 39)( 10, 49)( 11, 47)( 12, 54)( 13, 46)( 14, 53)( 15, 51)( 16, 52)
( 17, 50)( 18, 48)( 19, 67)( 20, 65)( 21, 72)( 22, 64)( 23, 71)( 24, 69)
( 25, 70)( 26, 68)( 27, 66)( 28, 58)( 29, 56)( 30, 63)( 31, 55)( 32, 62)
( 33, 60)( 34, 61)( 35, 59)( 36, 57)( 73, 76)( 75, 81)( 77, 80)( 82, 85)
( 84, 90)( 86, 89)( 91,103)( 92,101)( 93,108)( 94,100)( 95,107)( 96,105)
( 97,106)( 98,104)( 99,102)(109,112)(111,117)(113,116)(118,121)(120,126)
(122,125)(127,139)(128,137)(129,144)(130,136)(131,143)(132,141)(133,142)
(134,140)(135,138);;
s2 := (  1, 73)(  2, 74)(  3, 75)(  4, 81)(  5, 79)(  6, 80)(  7, 77)(  8, 78)
(  9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)( 16, 86)
( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)( 24, 98)
( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)( 32,106)
( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)( 40,144)
( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)( 48,129)
( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)( 56,119)
( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)( 64,109)
( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)( 72,112);;
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*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(144)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)
( 44, 69)( 45, 68)( 46, 55)( 47, 57)( 48, 56)( 49, 61)( 50, 63)( 51, 62)
( 52, 58)( 53, 60)( 54, 59)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)
(114,143)(115,139)(116,141)(117,140)(118,127)(119,129)(120,128)(121,133)
(122,135)(123,134)(124,130)(125,132)(126,131);
s1 := Sym(144)!(  1, 40)(  2, 38)(  3, 45)(  4, 37)(  5, 44)(  6, 42)(  7, 43)
(  8, 41)(  9, 39)( 10, 49)( 11, 47)( 12, 54)( 13, 46)( 14, 53)( 15, 51)
( 16, 52)( 17, 50)( 18, 48)( 19, 67)( 20, 65)( 21, 72)( 22, 64)( 23, 71)
( 24, 69)( 25, 70)( 26, 68)( 27, 66)( 28, 58)( 29, 56)( 30, 63)( 31, 55)
( 32, 62)( 33, 60)( 34, 61)( 35, 59)( 36, 57)( 73, 76)( 75, 81)( 77, 80)
( 82, 85)( 84, 90)( 86, 89)( 91,103)( 92,101)( 93,108)( 94,100)( 95,107)
( 96,105)( 97,106)( 98,104)( 99,102)(109,112)(111,117)(113,116)(118,121)
(120,126)(122,125)(127,139)(128,137)(129,144)(130,136)(131,143)(132,141)
(133,142)(134,140)(135,138);
s2 := Sym(144)!(  1, 73)(  2, 74)(  3, 75)(  4, 81)(  5, 79)(  6, 80)(  7, 77)
(  8, 78)(  9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)
( 16, 86)( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)
( 24, 98)( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)
( 32,106)( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)
( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)
( 48,129)( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)
( 56,119)( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)
( 64,109)( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)
( 72,112);
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*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s1 >; 
 
References : None.
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