Polytope of Type {2,24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,12}*1152f
if this polytope has a name.
Group : SmallGroup(1152,98805)
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
   3-fold quotients : {2,8,12}*384b
   4-fold quotients : {2,6,12}*288b, {2,12,6}*288c
   6-fold quotients : {2,4,12}*192a
   8-fold quotients : {2,6,6}*144b
   9-fold quotients : {2,8,4}*128b
   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
   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)( 21, 30)( 22, 32)
( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)
( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)
( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)
( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)
( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)
(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)
(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)
(127,146)(128,145);;
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)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)( 26,110)
( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)( 34, 99)
( 35,101)( 36, 97)( 37, 96)( 38, 98)( 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)( 57,130)( 58,129)
( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)( 66,139)
( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)( 74,143);;
s3 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)( 28, 38)
( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)( 45, 54)
( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)
( 68, 70)( 73, 74)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)
( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)( 88,140)
( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)( 96,111)
( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)(104,124)
(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);;
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*s1*s2*s3*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)( 21, 30)
( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)
( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)
( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)
( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)
( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)
( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)
(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)
(126,144)(127,146)(128,145);
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)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)
( 26,110)( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)
( 34, 99)( 35,101)( 36, 97)( 37, 96)( 38, 98)( 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)( 57,130)
( 58,129)( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)
( 66,139)( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)
( 74,143);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 36)
( 28, 38)( 29, 37)( 39, 51)( 40, 53)( 41, 52)( 42, 48)( 43, 50)( 44, 49)
( 45, 54)( 46, 56)( 47, 55)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)
( 67, 71)( 68, 70)( 73, 74)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)
( 80,130)( 81,135)( 82,137)( 83,136)( 84,141)( 85,143)( 86,142)( 87,138)
( 88,140)( 89,139)( 90,144)( 91,146)( 92,145)( 93,114)( 94,116)( 95,115)
( 96,111)( 97,113)( 98,112)( 99,117)(100,119)(101,118)(102,123)(103,125)
(104,124)(105,120)(106,122)(107,121)(108,126)(109,128)(110,127);
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*s1*s2*s3*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