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Polytope of Type {2,48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,133450)
Rank : 4
Schlafli Type : {2,48,6}
Number of vertices, edges, etc : 2, 48, 144, 6
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 : {2,24,6}*576c
   3-fold quotients : {2,16,6}*384
   4-fold quotients : {2,12,6}*288c
   6-fold quotients : {2,8,6}*192
   8-fold quotients : {2,6,6}*144b
   9-fold quotients : {2,16,2}*128
   12-fold quotients : {2,4,6}*96a
   16-fold quotients : {2,6,3}*72
   18-fold quotients : {2,8,2}*64
   24-fold quotients : {2,2,6}*48
   36-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,3}*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)(  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);;
s2 := (  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)
( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)( 26,110)
( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)( 34, 99)
( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,130)( 40,129)( 41,131)( 42,136)
( 43,135)( 44,137)( 45,133)( 46,132)( 47,134)( 48,139)( 49,138)( 50,140)
( 51,145)( 52,144)( 53,146)( 54,142)( 55,141)( 56,143)( 57,112)( 58,111)
( 59,113)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116)( 66,121)
( 67,120)( 68,122)( 69,127)( 70,126)( 71,128)( 72,124)( 73,123)( 74,125);;
s3 := (  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)( 19, 20)
( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)( 37, 38)
( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)( 55, 56)
( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 73, 74)
( 75, 78)( 76, 80)( 77, 79)( 82, 83)( 84, 87)( 85, 89)( 86, 88)( 91, 92)
( 93, 96)( 94, 98)( 95, 97)(100,101)(102,105)(103,107)(104,106)(109,110)
(111,114)(112,116)(113,115)(118,119)(120,123)(121,125)(122,124)(127,128)
(129,132)(130,134)(131,133)(136,137)(138,141)(139,143)(140,142)(145,146);;
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*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)(  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);
s2 := Sym(146)!(  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)
( 10, 78)( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21,103)( 22,102)( 23,104)( 24,109)( 25,108)
( 26,110)( 27,106)( 28,105)( 29,107)( 30, 94)( 31, 93)( 32, 95)( 33,100)
( 34, 99)( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,130)( 40,129)( 41,131)
( 42,136)( 43,135)( 44,137)( 45,133)( 46,132)( 47,134)( 48,139)( 49,138)
( 50,140)( 51,145)( 52,144)( 53,146)( 54,142)( 55,141)( 56,143)( 57,112)
( 58,111)( 59,113)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116)
( 66,121)( 67,120)( 68,122)( 69,127)( 70,126)( 71,128)( 72,124)( 73,123)
( 74,125);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)( 10, 11)( 12, 15)( 13, 17)( 14, 16)
( 19, 20)( 21, 24)( 22, 26)( 23, 25)( 28, 29)( 30, 33)( 31, 35)( 32, 34)
( 37, 38)( 39, 42)( 40, 44)( 41, 43)( 46, 47)( 48, 51)( 49, 53)( 50, 52)
( 55, 56)( 57, 60)( 58, 62)( 59, 61)( 64, 65)( 66, 69)( 67, 71)( 68, 70)
( 73, 74)( 75, 78)( 76, 80)( 77, 79)( 82, 83)( 84, 87)( 85, 89)( 86, 88)
( 91, 92)( 93, 96)( 94, 98)( 95, 97)(100,101)(102,105)(103,107)(104,106)
(109,110)(111,114)(112,116)(113,115)(118,119)(120,123)(121,125)(122,124)
(127,128)(129,132)(130,134)(131,133)(136,137)(138,141)(139,143)(140,142)
(145,146);
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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