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Polytope of Type {2,24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,97547)
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 : {2,24,6}*576b, {2,12,12}*576c
   3-fold quotients : {2,24,4}*384a
   4-fold quotients : {2,12,6}*288b, {2,6,12}*288c
   6-fold quotients : {2,12,4}*192a, {2,24,2}*192
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,8,4}*128a
   12-fold quotients : {2,12,2}*96, {2,6,4}*96a
   16-fold quotients : {2,3,6}*72
   18-fold quotients : {2,4,4}*64, {2,8,2}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,3,2}*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)(  6,  9)(  7, 11)(  8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)
( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)( 46, 53)
( 47, 52)( 57, 66)( 58, 68)( 59, 67)( 60, 72)( 61, 74)( 62, 73)( 63, 69)
( 64, 71)( 65, 70)( 75,129)( 76,131)( 77,130)( 78,135)( 79,137)( 80,136)
( 81,132)( 82,134)( 83,133)( 84,138)( 85,140)( 86,139)( 87,144)( 88,146)
( 89,145)( 90,141)( 91,143)( 92,142)( 93,111)( 94,113)( 95,112)( 96,117)
( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)(104,121)
(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);;
s2 := (  3, 79)(  4, 78)(  5, 80)(  6, 76)(  7, 75)(  8, 77)(  9, 82)( 10, 81)
( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)
( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)
( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)( 34,102)
( 35,104)( 36,109)( 37,108)( 38,110)( 39,124)( 40,123)( 41,125)( 42,121)
( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)
( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,142)( 58,141)
( 59,143)( 60,139)( 61,138)( 62,140)( 63,145)( 64,144)( 65,146)( 66,133)
( 67,132)( 68,134)( 69,130)( 70,129)( 71,131)( 72,136)( 73,135)( 74,137);;
s3 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 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);;
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*s3*s1*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  6,  9)(  7, 11)(  8, 10)( 13, 14)( 15, 18)( 16, 20)
( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)
( 35, 37)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)
( 46, 53)( 47, 52)( 57, 66)( 58, 68)( 59, 67)( 60, 72)( 61, 74)( 62, 73)
( 63, 69)( 64, 71)( 65, 70)( 75,129)( 76,131)( 77,130)( 78,135)( 79,137)
( 80,136)( 81,132)( 82,134)( 83,133)( 84,138)( 85,140)( 86,139)( 87,144)
( 88,146)( 89,145)( 90,141)( 91,143)( 92,142)( 93,111)( 94,113)( 95,112)
( 96,117)( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)
(104,121)(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);
s2 := Sym(146)!(  3, 79)(  4, 78)(  5, 80)(  6, 76)(  7, 75)(  8, 77)(  9, 82)
( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)
( 18, 91)( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)
( 26, 95)( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)
( 34,102)( 35,104)( 36,109)( 37,108)( 38,110)( 39,124)( 40,123)( 41,125)
( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)
( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,142)
( 58,141)( 59,143)( 60,139)( 61,138)( 62,140)( 63,145)( 64,144)( 65,146)
( 66,133)( 67,132)( 68,134)( 69,130)( 70,129)( 71,131)( 72,136)( 73,135)
( 74,137);
s3 := 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)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 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);
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*s3*s1*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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