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Polytope of Type {2,6,24}

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

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