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Polytope of Type {2,6,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,48}*1152a
if this polytope has a name.
Group : SmallGroup(1152,133450)
Rank : 4
Schlafli Type : {2,6,48}
Number of vertices, edges, etc : 2, 6, 144, 48
Order of s0s1s2s3 : 48
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 : {2,6,24}*576c
   3-fold quotients : {2,6,16}*384
   4-fold quotients : {2,6,12}*288c
   6-fold quotients : {2,6,8}*192
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,2,16}*128
   12-fold quotients : {2,6,4}*96a
   16-fold quotients : {2,3,6}*72
   18-fold quotients : {2,2,8}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*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)
( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)
( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)
( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)( 89, 91)
( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)(107,109)
(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)(125,127)
(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)(143,145);;
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)( 39,133)( 40,132)( 41,134)( 42,130)
( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)( 50,143)
( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)( 58,114)
( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)( 66,124)
( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)( 74,128);;
s3 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)
( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 39, 57)
( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)( 47, 64)
( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)( 55, 74)
( 56, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)
( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)( 89,124)
( 90,126)( 91,128)( 92,127)( 93,138)( 94,140)( 95,139)( 96,141)( 97,143)
( 98,142)( 99,144)(100,146)(101,145)(102,129)(103,131)(104,130)(105,132)
(106,134)(107,133)(108,135)(109,137)(110,136);;
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*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)
( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)
( 71, 73)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)
( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)
(107,109)(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)
(125,127)(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)
(143,145);
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)( 39,133)( 40,132)( 41,134)
( 42,130)( 43,129)( 44,131)( 45,136)( 46,135)( 47,137)( 48,142)( 49,141)
( 50,143)( 51,139)( 52,138)( 53,140)( 54,145)( 55,144)( 56,146)( 57,115)
( 58,114)( 59,116)( 60,112)( 61,111)( 62,113)( 63,118)( 64,117)( 65,119)
( 66,124)( 67,123)( 68,125)( 69,121)( 70,120)( 71,122)( 72,127)( 73,126)
( 74,128);
s3 := Sym(146)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)
( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)
( 39, 57)( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)
( 47, 64)( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)
( 55, 74)( 56, 73)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)
( 81,117)( 82,119)( 83,118)( 84,120)( 85,122)( 86,121)( 87,123)( 88,125)
( 89,124)( 90,126)( 91,128)( 92,127)( 93,138)( 94,140)( 95,139)( 96,141)
( 97,143)( 98,142)( 99,144)(100,146)(101,145)(102,129)(103,131)(104,130)
(105,132)(106,134)(107,133)(108,135)(109,137)(110,136);
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*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 

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