Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*576c
if this polytope has a name.
Group : SmallGroup(576,2292)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 24, 144, 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 :
   {12,12,2} of size 1152
Vertex Figure Of :
   {2,12,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*288c
   3-fold quotients : {12,4}*192a
   4-fold quotients : {12,6}*144b, {6,12}*144c
   6-fold quotients : {12,4}*96a
   8-fold quotients : {6,6}*72c
   9-fold quotients : {4,4}*64
   12-fold quotients : {12,2}*48, {6,4}*48a
   16-fold quotients : {3,6}*36
   18-fold quotients : {4,4}*32
   24-fold quotients : {6,2}*24
   36-fold quotients : {2,4}*16, {4,2}*16
   48-fold quotients : {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,12}*1152a, {12,24}*1152c, {12,12}*1152a, {12,24}*1152d, {24,12}*1152f
   3-fold covers : {36,12}*1728b, {12,12}*1728a, {12,12}*1728h
Permutation Representation (GAP) :

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

References : None.
to this polytope