Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*576f
if this polytope has a name.
Group : SmallGroup(576,2897)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 24, 144, 12
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,12,2} of size 1152
Vertex Figure Of :
   {2,24,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*288c
   3-fold quotients : {24,4}*192b
   4-fold quotients : {12,6}*144b, {6,12}*144c
   6-fold quotients : {12,4}*96a
   8-fold quotients : {6,6}*72c
   9-fold quotients : {8,4}*64b
   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, {24,24}*1152d, {24,24}*1152l
   3-fold covers : {72,12}*1728d, {24,12}*1728e, {24,12}*1728p
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, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)
( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)( 61, 67)
( 62, 69)( 63, 68)( 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)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)( 24,102)
( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)( 32, 91)
( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 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)( 55,140)( 56,139)
( 57,141)( 58,137)( 59,136)( 60,138)( 61,143)( 62,142)( 63,144)( 64,131)
( 65,130)( 66,132)( 67,128)( 68,127)( 69,129)( 70,134)( 71,133)( 72,135);;
s2 := (  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)( 20, 29)
( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)( 40, 43)
( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 55, 64)( 56, 65)( 57, 66)
( 58, 70)( 59, 71)( 60, 72)( 61, 67)( 62, 68)( 63, 69)( 73,109)( 74,110)
( 75,111)( 76,115)( 77,116)( 78,117)( 79,112)( 80,113)( 81,114)( 82,118)
( 83,119)( 84,120)( 85,124)( 86,125)( 87,126)( 88,121)( 89,122)( 90,123)
( 91,136)( 92,137)( 93,138)( 94,142)( 95,143)( 96,144)( 97,139)( 98,140)
( 99,141)(100,127)(101,128)(102,129)(103,133)(104,134)(105,135)(106,130)
(107,131)(108,132);;
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, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)
( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)
( 61, 67)( 62, 69)( 63, 68)( 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)( 19,104)( 20,103)( 21,105)( 22,101)( 23,100)
( 24,102)( 25,107)( 26,106)( 27,108)( 28, 95)( 29, 94)( 30, 96)( 31, 92)
( 32, 91)( 33, 93)( 34, 98)( 35, 97)( 36, 99)( 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)( 55,140)
( 56,139)( 57,141)( 58,137)( 59,136)( 60,138)( 61,143)( 62,142)( 63,144)
( 64,131)( 65,130)( 66,132)( 67,128)( 68,127)( 69,129)( 70,134)( 71,133)
( 72,135);
s2 := Sym(144)!(  4,  7)(  5,  8)(  6,  9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)
( 20, 29)( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)
( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 55, 64)( 56, 65)
( 57, 66)( 58, 70)( 59, 71)( 60, 72)( 61, 67)( 62, 68)( 63, 69)( 73,109)
( 74,110)( 75,111)( 76,115)( 77,116)( 78,117)( 79,112)( 80,113)( 81,114)
( 82,118)( 83,119)( 84,120)( 85,124)( 86,125)( 87,126)( 88,121)( 89,122)
( 90,123)( 91,136)( 92,137)( 93,138)( 94,142)( 95,143)( 96,144)( 97,139)
( 98,140)( 99,141)(100,127)(101,128)(102,129)(103,133)(104,134)(105,135)
(106,130)(107,131)(108,132);
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, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope