Polytope of Type {6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*576d
if this polytope has a name.
Group : SmallGroup(576,8328)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 12, 144, 48
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,24,2} of size 1152
Vertex Figure Of :
   {2,6,24} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*288b
   3-fold quotients : {6,8}*192c
   4-fold quotients : {3,12}*144
   6-fold quotients : {6,4}*96
   8-fold quotients : {6,6}*72c
   12-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,6}*36
   24-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,24}*1152j, {12,24}*1152n, {6,24}*1152l
   3-fold covers : {18,24}*1728d, {6,24}*1728d, {6,24}*1728g
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope