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Polytope of Type {2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157582)
Rank : 4
Schlafli Type : {2,6,6}
Number of vertices, edges, etc : 2, 48, 144, 48
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 : {2,6,6}*576b
   3-fold quotients : {2,6,6}*384b
   4-fold quotients : {2,3,6}*288
   6-fold quotients : {2,6,6}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*48, {2,6,2}*48
   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 := (  3, 75)(  4, 76)(  5, 80)(  6, 79)(  7, 78)(  8, 77)(  9, 82)( 10, 81)
( 11, 91)( 12, 92)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 98)( 18, 97)
( 19, 83)( 20, 84)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 90)( 26, 89)
( 27,123)( 28,124)( 29,128)( 30,127)( 31,126)( 32,125)( 33,130)( 34,129)
( 35,139)( 36,140)( 37,144)( 38,143)( 39,142)( 40,141)( 41,146)( 42,145)
( 43,131)( 44,132)( 45,136)( 46,135)( 47,134)( 48,133)( 49,138)( 50,137)
( 51, 99)( 52,100)( 53,104)( 54,103)( 55,102)( 56,101)( 57,106)( 58,105)
( 59,115)( 60,116)( 61,120)( 62,119)( 63,118)( 64,117)( 65,122)( 66,121)
( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113);;
s2 := (  3, 35)(  4, 36)(  5, 38)(  6, 37)(  7, 41)(  8, 42)(  9, 39)( 10, 40)
( 11, 27)( 12, 28)( 13, 30)( 14, 29)( 15, 33)( 16, 34)( 17, 31)( 18, 32)
( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)( 26, 48)
( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 65)( 56, 66)( 57, 63)( 58, 64)
( 69, 70)( 71, 73)( 72, 74)( 75,107)( 76,108)( 77,110)( 78,109)( 79,113)
( 80,114)( 81,111)( 82,112)( 83, 99)( 84,100)( 85,102)( 86,101)( 87,105)
( 88,106)( 89,103)( 90,104)( 91,115)( 92,116)( 93,118)( 94,117)( 95,121)
( 96,122)( 97,119)( 98,120)(123,131)(124,132)(125,134)(126,133)(127,137)
(128,138)(129,135)(130,136)(141,142)(143,145)(144,146);;
s3 := (  3,  9)(  4, 10)(  7,  8)( 11, 17)( 12, 18)( 15, 16)( 19, 25)( 20, 26)
( 23, 24)( 27, 57)( 28, 58)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 51)
( 34, 52)( 35, 65)( 36, 66)( 37, 61)( 38, 62)( 39, 64)( 40, 63)( 41, 59)
( 42, 60)( 43, 73)( 44, 74)( 45, 69)( 46, 70)( 47, 72)( 48, 71)( 49, 67)
( 50, 68)( 75, 82)( 76, 81)( 77, 78)( 83, 90)( 84, 89)( 85, 86)( 91, 98)
( 92, 97)( 93, 94)( 99,130)(100,129)(101,126)(102,125)(103,127)(104,128)
(105,124)(106,123)(107,138)(108,137)(109,134)(110,133)(111,135)(112,136)
(113,132)(114,131)(115,146)(116,145)(117,142)(118,141)(119,143)(120,144)
(121,140)(122,139);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  3, 75)(  4, 76)(  5, 80)(  6, 79)(  7, 78)(  8, 77)(  9, 82)
( 10, 81)( 11, 91)( 12, 92)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 98)
( 18, 97)( 19, 83)( 20, 84)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 90)
( 26, 89)( 27,123)( 28,124)( 29,128)( 30,127)( 31,126)( 32,125)( 33,130)
( 34,129)( 35,139)( 36,140)( 37,144)( 38,143)( 39,142)( 40,141)( 41,146)
( 42,145)( 43,131)( 44,132)( 45,136)( 46,135)( 47,134)( 48,133)( 49,138)
( 50,137)( 51, 99)( 52,100)( 53,104)( 54,103)( 55,102)( 56,101)( 57,106)
( 58,105)( 59,115)( 60,116)( 61,120)( 62,119)( 63,118)( 64,117)( 65,122)
( 66,121)( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)
( 74,113);
s2 := Sym(146)!(  3, 35)(  4, 36)(  5, 38)(  6, 37)(  7, 41)(  8, 42)(  9, 39)
( 10, 40)( 11, 27)( 12, 28)( 13, 30)( 14, 29)( 15, 33)( 16, 34)( 17, 31)
( 18, 32)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)
( 26, 48)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 55, 65)( 56, 66)( 57, 63)
( 58, 64)( 69, 70)( 71, 73)( 72, 74)( 75,107)( 76,108)( 77,110)( 78,109)
( 79,113)( 80,114)( 81,111)( 82,112)( 83, 99)( 84,100)( 85,102)( 86,101)
( 87,105)( 88,106)( 89,103)( 90,104)( 91,115)( 92,116)( 93,118)( 94,117)
( 95,121)( 96,122)( 97,119)( 98,120)(123,131)(124,132)(125,134)(126,133)
(127,137)(128,138)(129,135)(130,136)(141,142)(143,145)(144,146);
s3 := Sym(146)!(  3,  9)(  4, 10)(  7,  8)( 11, 17)( 12, 18)( 15, 16)( 19, 25)
( 20, 26)( 23, 24)( 27, 57)( 28, 58)( 29, 53)( 30, 54)( 31, 56)( 32, 55)
( 33, 51)( 34, 52)( 35, 65)( 36, 66)( 37, 61)( 38, 62)( 39, 64)( 40, 63)
( 41, 59)( 42, 60)( 43, 73)( 44, 74)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 49, 67)( 50, 68)( 75, 82)( 76, 81)( 77, 78)( 83, 90)( 84, 89)( 85, 86)
( 91, 98)( 92, 97)( 93, 94)( 99,130)(100,129)(101,126)(102,125)(103,127)
(104,128)(105,124)(106,123)(107,138)(108,137)(109,134)(110,133)(111,135)
(112,136)(113,132)(114,131)(115,146)(116,145)(117,142)(118,141)(119,143)
(120,144)(121,140)(122,139);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2 >; 
 

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