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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}*1152e
if this polytope has a name.
Group : SmallGroup(1152,98801)
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}*576c
   3-fold quotients : {2,24,4}*384b
   4-fold quotients : {2,12,6}*288b, {2,6,12}*288c
   6-fold quotients : {2,12,4}*192a
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,8,4}*128b
   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
   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)( 75,138)( 76,140)( 77,139)( 78,144)( 79,146)( 80,145)
( 81,141)( 82,143)( 83,142)( 84,129)( 85,131)( 86,130)( 87,135)( 88,137)
( 89,136)( 90,132)( 91,134)( 92,133)( 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)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)
( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)
( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,115)( 40,114)( 41,116)( 42,112)
( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)( 50,125)
( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 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 := (  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)( 22, 31)
( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)( 42, 45)
( 43, 46)( 44, 47)( 51, 54)( 52, 55)( 53, 56)( 57, 66)( 58, 67)( 59, 68)
( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75,111)( 76,112)
( 77,113)( 78,117)( 79,118)( 80,119)( 81,114)( 82,115)( 83,116)( 84,120)
( 85,121)( 86,122)( 87,126)( 88,127)( 89,128)( 90,123)( 91,124)( 92,125)
( 93,138)( 94,139)( 95,140)( 96,144)( 97,145)( 98,146)( 99,141)(100,142)
(101,143)(102,129)(103,130)(104,131)(105,135)(106,136)(107,137)(108,132)
(109,133)(110,134);;
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*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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)( 75,138)( 76,140)( 77,139)( 78,144)( 79,146)
( 80,145)( 81,141)( 82,143)( 83,142)( 84,129)( 85,131)( 86,130)( 87,135)
( 88,137)( 89,136)( 90,132)( 91,134)( 92,133)( 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)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)
( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)
( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,115)( 40,114)( 41,116)
( 42,112)( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)
( 50,125)( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 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)!(  6,  9)(  7, 10)(  8, 11)( 15, 18)( 16, 19)( 17, 20)( 21, 30)
( 22, 31)( 23, 32)( 24, 36)( 25, 37)( 26, 38)( 27, 33)( 28, 34)( 29, 35)
( 42, 45)( 43, 46)( 44, 47)( 51, 54)( 52, 55)( 53, 56)( 57, 66)( 58, 67)
( 59, 68)( 60, 72)( 61, 73)( 62, 74)( 63, 69)( 64, 70)( 65, 71)( 75,111)
( 76,112)( 77,113)( 78,117)( 79,118)( 80,119)( 81,114)( 82,115)( 83,116)
( 84,120)( 85,121)( 86,122)( 87,126)( 88,127)( 89,128)( 90,123)( 91,124)
( 92,125)( 93,138)( 94,139)( 95,140)( 96,144)( 97,145)( 98,146)( 99,141)
(100,142)(101,143)(102,129)(103,130)(104,131)(105,135)(106,136)(107,137)
(108,132)(109,133)(110,134);
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*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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