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Polytope of Type {2,8,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,9}*1152
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 4
Schlafli Type : {2,8,9}
Number of vertices, edges, etc : 2, 32, 144, 36
Order of s0s1s2s3 : 18
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) :
   3-fold quotients : {2,8,3}*384
   4-fold quotients : {2,4,9}*288
   8-fold quotients : {2,4,9}*144
   12-fold quotients : {2,4,3}*96
   16-fold quotients : {2,2,9}*72
   24-fold quotients : {2,4,3}*48
   48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 34)( 24, 33)( 25, 32)( 26, 31)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 50)( 40, 49)( 41, 48)( 42, 47)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 82)( 72, 81)( 73, 80)( 74, 79)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 98)( 88, 97)( 89, 96)( 90, 95)
( 99,107)(100,108)(101,109)(102,110)(103,114)(104,113)(105,112)(106,111)
(115,123)(116,124)(117,125)(118,126)(119,130)(120,129)(121,128)(122,127)
(131,139)(132,140)(133,141)(134,142)(135,146)(136,145)(137,144)(138,143);;
s2 := (  5,  6)(  7, 12)(  8, 11)(  9, 13)( 10, 14)( 17, 18)( 19, 35)( 20, 36)
( 21, 38)( 22, 37)( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 40)( 28, 39)
( 29, 41)( 30, 42)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)( 52,116)
( 53,118)( 54,117)( 55,124)( 56,123)( 57,125)( 58,126)( 59,120)( 60,119)
( 61,121)( 62,122)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)( 68,100)
( 69,102)( 70,101)( 71,108)( 72,107)( 73,109)( 74,110)( 75,104)( 76,103)
( 77,105)( 78,106)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)( 84,132)
( 85,134)( 86,133)( 87,140)( 88,139)( 89,141)( 90,142)( 91,136)( 92,135)
( 93,137)( 94,138)( 95,143)( 96,144)( 97,146)( 98,145);;
s3 := (  3,107)(  4,110)(  5,109)(  6,108)(  7,105)(  8,104)(  9,103)( 10,106)
( 11, 99)( 12,102)( 13,101)( 14,100)( 15,111)( 16,114)( 17,113)( 18,112)
( 19,139)( 20,142)( 21,141)( 22,140)( 23,137)( 24,136)( 25,135)( 26,138)
( 27,131)( 28,134)( 29,133)( 30,132)( 31,143)( 32,146)( 33,145)( 34,144)
( 35,123)( 36,126)( 37,125)( 38,124)( 39,121)( 40,120)( 41,119)( 42,122)
( 43,115)( 44,118)( 45,117)( 46,116)( 47,127)( 48,130)( 49,129)( 50,128)
( 51, 59)( 52, 62)( 53, 61)( 54, 60)( 55, 57)( 64, 66)( 67, 91)( 68, 94)
( 69, 93)( 70, 92)( 71, 89)( 72, 88)( 73, 87)( 74, 90)( 75, 83)( 76, 86)
( 77, 85)( 78, 84)( 79, 95)( 80, 98)( 81, 97)( 82, 96);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 34)( 24, 33)( 25, 32)
( 26, 31)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 50)( 40, 49)( 41, 48)
( 42, 47)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 66)( 56, 65)( 57, 64)
( 58, 63)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 82)( 72, 81)( 73, 80)
( 74, 79)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 98)( 88, 97)( 89, 96)
( 90, 95)( 99,107)(100,108)(101,109)(102,110)(103,114)(104,113)(105,112)
(106,111)(115,123)(116,124)(117,125)(118,126)(119,130)(120,129)(121,128)
(122,127)(131,139)(132,140)(133,141)(134,142)(135,146)(136,145)(137,144)
(138,143);
s2 := Sym(146)!(  5,  6)(  7, 12)(  8, 11)(  9, 13)( 10, 14)( 17, 18)( 19, 35)
( 20, 36)( 21, 38)( 22, 37)( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 40)
( 28, 39)( 29, 41)( 30, 42)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)
( 52,116)( 53,118)( 54,117)( 55,124)( 56,123)( 57,125)( 58,126)( 59,120)
( 60,119)( 61,121)( 62,122)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)
( 68,100)( 69,102)( 70,101)( 71,108)( 72,107)( 73,109)( 74,110)( 75,104)
( 76,103)( 77,105)( 78,106)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)
( 84,132)( 85,134)( 86,133)( 87,140)( 88,139)( 89,141)( 90,142)( 91,136)
( 92,135)( 93,137)( 94,138)( 95,143)( 96,144)( 97,146)( 98,145);
s3 := Sym(146)!(  3,107)(  4,110)(  5,109)(  6,108)(  7,105)(  8,104)(  9,103)
( 10,106)( 11, 99)( 12,102)( 13,101)( 14,100)( 15,111)( 16,114)( 17,113)
( 18,112)( 19,139)( 20,142)( 21,141)( 22,140)( 23,137)( 24,136)( 25,135)
( 26,138)( 27,131)( 28,134)( 29,133)( 30,132)( 31,143)( 32,146)( 33,145)
( 34,144)( 35,123)( 36,126)( 37,125)( 38,124)( 39,121)( 40,120)( 41,119)
( 42,122)( 43,115)( 44,118)( 45,117)( 46,116)( 47,127)( 48,130)( 49,129)
( 50,128)( 51, 59)( 52, 62)( 53, 61)( 54, 60)( 55, 57)( 64, 66)( 67, 91)
( 68, 94)( 69, 93)( 70, 92)( 71, 89)( 72, 88)( 73, 87)( 74, 90)( 75, 83)
( 76, 86)( 77, 85)( 78, 84)( 79, 95)( 80, 98)( 81, 97)( 82, 96);
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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