Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*576b
if this polytope has a name.
Group : SmallGroup(576,8313)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 24, 144, 48
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,12,2} of size 1152
Vertex Figure Of :
   {2,6,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*288a
   3-fold quotients : {6,4}*192b
   4-fold quotients : {6,12}*144a, {6,12}*144d
   6-fold quotients : {6,4}*96
   8-fold quotients : {6,6}*72a
   12-fold quotients : {2,12}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   36-fold quotients : {2,4}*16
   48-fold quotients : {2,3}*12, {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,24}*1152d, {6,24}*1152h, {6,12}*1152d, {12,12}*1152h, {12,12}*1152k
   3-fold covers : {6,36}*1728b, {18,12}*1728c, {6,12}*1728b, {6,12}*1728i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope