Polytope of Type {2,24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,97551)
Rank : 4
Schlafli Type : {2,24,12}
Number of vertices, edges, etc : 2, 24, 144, 12
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,12}*576b, {2,24,6}*576c
   3-fold quotients : {2,8,12}*384a
   4-fold quotients : {2,6,12}*288b, {2,12,6}*288c
   6-fold quotients : {2,4,12}*192a, {2,8,6}*192
   8-fold quotients : {2,6,6}*144b
   9-fold quotients : {2,8,4}*128a
   12-fold quotients : {2,2,12}*96, {2,4,6}*96a
   16-fold quotients : {2,6,3}*72
   18-fold quotients : {2,4,4}*64, {2,8,2}*64
   24-fold quotients : {2,2,6}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)( 42, 51)
( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)( 59, 67)
( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75,111)( 76,113)
( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,119)( 83,118)( 84,120)
( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)( 90,126)( 91,128)( 92,127)
( 93,129)( 94,131)( 95,130)( 96,132)( 97,134)( 98,133)( 99,135)(100,137)
(101,136)(102,138)(103,140)(104,139)(105,141)(106,143)(107,142)(108,144)
(109,146)(110,145);;
s2 := (  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)
( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)
( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)
( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)( 42,127)
( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)( 50,113)
( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)( 58,138)
( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)( 66,130)
( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)( 74,134);;
s3 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)
( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)( 55, 56)
( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)
( 75, 96)( 76, 98)( 77, 97)( 78, 93)( 79, 95)( 80, 94)( 81, 99)( 82,101)
( 83,100)( 84,105)( 85,107)( 86,106)( 87,102)( 88,104)( 89,103)( 90,108)
( 91,110)( 92,109)(111,132)(112,134)(113,133)(114,129)(115,131)(116,130)
(117,135)(118,137)(119,136)(120,141)(121,143)(122,142)(123,138)(124,140)
(125,139)(126,144)(127,146)(128,145);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)
( 42, 51)( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)
( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75,111)
( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,119)( 83,118)
( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)( 90,126)( 91,128)
( 92,127)( 93,129)( 94,131)( 95,130)( 96,132)( 97,134)( 98,133)( 99,135)
(100,137)(101,136)(102,138)(103,140)(104,139)(105,141)(106,143)(107,142)
(108,144)(109,146)(110,145);
s2 := Sym(146)!(  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)
( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)
( 26,101)( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)
( 34,108)( 35,110)( 36,106)( 37,105)( 38,107)( 39,121)( 40,120)( 41,122)
( 42,127)( 43,126)( 44,128)( 45,124)( 46,123)( 47,125)( 48,112)( 49,111)
( 50,113)( 51,118)( 52,117)( 53,119)( 54,115)( 55,114)( 56,116)( 57,139)
( 58,138)( 59,140)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)
( 66,130)( 67,129)( 68,131)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)
( 74,134);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)
( 37, 38)( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)
( 55, 56)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)
( 73, 74)( 75, 96)( 76, 98)( 77, 97)( 78, 93)( 79, 95)( 80, 94)( 81, 99)
( 82,101)( 83,100)( 84,105)( 85,107)( 86,106)( 87,102)( 88,104)( 89,103)
( 90,108)( 91,110)( 92,109)(111,132)(112,134)(113,133)(114,129)(115,131)
(116,130)(117,135)(118,137)(119,136)(120,141)(121,143)(122,142)(123,138)
(124,140)(125,139)(126,144)(127,146)(128,145);
poly := sub<Sym(146)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope