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Polytope of Type {2,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,6}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 4
Schlafli Type : {2,24,6}
Number of vertices, edges, etc : 2, 48, 144, 12
Order of s0s1s2s3 : 12
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 : {2,12,6}*576a
   3-fold quotients : {2,8,6}*384b
   4-fold quotients : {2,12,6}*288d
   6-fold quotients : {2,8,3}*192, {2,4,6}*192
   8-fold quotients : {2,6,6}*144a
   12-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   24-fold quotients : {2,4,3}*48, {2,2,6}*48, {2,6,2}*48
   48-fold quotients : {2,2,3}*24, {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 := (  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)( 10, 78)
( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 92)( 16, 91)( 17, 93)( 18, 94)
( 19, 87)( 20, 88)( 21, 90)( 22, 89)( 23, 84)( 24, 83)( 25, 85)( 26, 86)
( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)( 34,102)
( 35,119)( 36,120)( 37,122)( 38,121)( 39,116)( 40,115)( 41,117)( 42,118)
( 43,111)( 44,112)( 45,114)( 46,113)( 47,108)( 48,107)( 49,109)( 50,110)
( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)( 58,126)
( 59,143)( 60,144)( 61,146)( 62,145)( 63,140)( 64,139)( 65,141)( 66,142)
( 67,135)( 68,136)( 69,138)( 70,137)( 71,132)( 72,131)( 73,133)( 74,134);;
s2 := (  3, 11)(  4, 12)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 18)( 10, 17)
( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)( 31, 62)
( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)
( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)( 79, 85)
( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)(100,131)
(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)(108,123)
(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)(116,139)
(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);;
s3 := (  3, 51)(  4, 52)(  5, 57)(  6, 58)(  7, 56)(  8, 55)(  9, 53)( 10, 54)
( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)( 18, 62)
( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)( 26, 70)
( 29, 33)( 30, 34)( 31, 32)( 37, 41)( 38, 42)( 39, 40)( 45, 49)( 46, 50)
( 47, 48)( 75,124)( 76,123)( 77,130)( 78,129)( 79,127)( 80,128)( 81,126)
( 82,125)( 83,132)( 84,131)( 85,138)( 86,137)( 87,135)( 88,136)( 89,134)
( 90,133)( 91,140)( 92,139)( 93,146)( 94,145)( 95,143)( 96,144)( 97,142)
( 98,141)( 99,100)(101,106)(102,105)(107,108)(109,114)(110,113)(115,116)
(117,122)(118,121);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)
( 10, 78)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 92)( 16, 91)( 17, 93)
( 18, 94)( 19, 87)( 20, 88)( 21, 90)( 22, 89)( 23, 84)( 24, 83)( 25, 85)
( 26, 86)( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)
( 34,102)( 35,119)( 36,120)( 37,122)( 38,121)( 39,116)( 40,115)( 41,117)
( 42,118)( 43,111)( 44,112)( 45,114)( 46,113)( 47,108)( 48,107)( 49,109)
( 50,110)( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)
( 58,126)( 59,143)( 60,144)( 61,146)( 62,145)( 63,140)( 64,139)( 65,141)
( 66,142)( 67,135)( 68,136)( 69,138)( 70,137)( 71,132)( 72,131)( 73,133)
( 74,134);
s2 := Sym(146)!(  3, 11)(  4, 12)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 18)
( 10, 17)( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)
( 31, 62)( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)
( 47, 70)( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)
( 79, 85)( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)
(100,131)(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)
(108,123)(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)
(116,139)(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);
s3 := Sym(146)!(  3, 51)(  4, 52)(  5, 57)(  6, 58)(  7, 56)(  8, 55)(  9, 53)
( 10, 54)( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)
( 18, 62)( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)
( 26, 70)( 29, 33)( 30, 34)( 31, 32)( 37, 41)( 38, 42)( 39, 40)( 45, 49)
( 46, 50)( 47, 48)( 75,124)( 76,123)( 77,130)( 78,129)( 79,127)( 80,128)
( 81,126)( 82,125)( 83,132)( 84,131)( 85,138)( 86,137)( 87,135)( 88,136)
( 89,134)( 90,133)( 91,140)( 92,139)( 93,146)( 94,145)( 95,143)( 96,144)
( 97,142)( 98,141)( 99,100)(101,106)(102,105)(107,108)(109,114)(110,113)
(115,116)(117,122)(118,121);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >; 
 

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