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Polytope of Type {2,16,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,18}*1152
if this polytope has a name.
Group : SmallGroup(1152,133439)
Rank : 4
Schlafli Type : {2,16,18}
Number of vertices, edges, etc : 2, 16, 144, 18
Order of s0s1s2s3 : 144
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 : {2,8,18}*576
   3-fold quotients : {2,16,6}*384
   4-fold quotients : {2,4,18}*288a
   6-fold quotients : {2,8,6}*192
   8-fold quotients : {2,2,18}*144
   9-fold quotients : {2,16,2}*128
   12-fold quotients : {2,4,6}*96a
   16-fold quotients : {2,2,9}*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 := ( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)( 28, 37)
( 29, 38)( 39, 57)( 40, 58)( 41, 59)( 42, 60)( 43, 61)( 44, 62)( 45, 63)
( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)( 51, 69)( 52, 70)( 53, 71)
( 54, 72)( 55, 73)( 56, 74)( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)
( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,138)( 94,139)( 95,140)
( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,129)(103,130)
(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137);;
s2 := (  3, 75)(  4, 77)(  5, 76)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)
( 11, 80)( 12, 84)( 13, 86)( 14, 85)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21,102)( 22,104)( 23,103)( 24,109)( 25,108)( 26,110)
( 27,106)( 28,105)( 29,107)( 30, 93)( 31, 95)( 32, 94)( 33,100)( 34, 99)
( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,129)( 40,131)( 41,130)( 42,136)
( 43,135)( 44,137)( 45,133)( 46,132)( 47,134)( 48,138)( 49,140)( 50,139)
( 51,145)( 52,144)( 53,146)( 54,142)( 55,141)( 56,143)( 57,111)( 58,113)
( 59,112)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116)( 66,120)
( 67,122)( 68,121)( 69,127)( 70,126)( 71,128)( 72,124)( 73,123)( 74,125);;
s3 := (  3,  6)(  4,  8)(  5,  7)(  9, 10)( 12, 15)( 13, 17)( 14, 16)( 18, 19)
( 21, 24)( 22, 26)( 23, 25)( 27, 28)( 30, 33)( 31, 35)( 32, 34)( 36, 37)
( 39, 42)( 40, 44)( 41, 43)( 45, 46)( 48, 51)( 49, 53)( 50, 52)( 54, 55)
( 57, 60)( 58, 62)( 59, 61)( 63, 64)( 66, 69)( 67, 71)( 68, 70)( 72, 73)
( 75, 78)( 76, 80)( 77, 79)( 81, 82)( 84, 87)( 85, 89)( 86, 88)( 90, 91)
( 93, 96)( 94, 98)( 95, 97)( 99,100)(102,105)(103,107)(104,106)(108,109)
(111,114)(112,116)(113,115)(117,118)(120,123)(121,125)(122,124)(126,127)
(129,132)(130,134)(131,133)(135,136)(138,141)(139,143)(140,142)(144,145);;
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*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)( 27, 36)
( 28, 37)( 29, 38)( 39, 57)( 40, 58)( 41, 59)( 42, 60)( 43, 61)( 44, 62)
( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)( 51, 69)( 52, 70)
( 53, 71)( 54, 72)( 55, 73)( 56, 74)( 75,111)( 76,112)( 77,113)( 78,114)
( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)
( 87,123)( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,138)( 94,139)
( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,129)
(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137);
s2 := Sym(146)!(  3, 75)(  4, 77)(  5, 76)(  6, 82)(  7, 81)(  8, 83)(  9, 79)
( 10, 78)( 11, 80)( 12, 84)( 13, 86)( 14, 85)( 15, 91)( 16, 90)( 17, 92)
( 18, 88)( 19, 87)( 20, 89)( 21,102)( 22,104)( 23,103)( 24,109)( 25,108)
( 26,110)( 27,106)( 28,105)( 29,107)( 30, 93)( 31, 95)( 32, 94)( 33,100)
( 34, 99)( 35,101)( 36, 97)( 37, 96)( 38, 98)( 39,129)( 40,131)( 41,130)
( 42,136)( 43,135)( 44,137)( 45,133)( 46,132)( 47,134)( 48,138)( 49,140)
( 50,139)( 51,145)( 52,144)( 53,146)( 54,142)( 55,141)( 56,143)( 57,111)
( 58,113)( 59,112)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116)
( 66,120)( 67,122)( 68,121)( 69,127)( 70,126)( 71,128)( 72,124)( 73,123)
( 74,125);
s3 := Sym(146)!(  3,  6)(  4,  8)(  5,  7)(  9, 10)( 12, 15)( 13, 17)( 14, 16)
( 18, 19)( 21, 24)( 22, 26)( 23, 25)( 27, 28)( 30, 33)( 31, 35)( 32, 34)
( 36, 37)( 39, 42)( 40, 44)( 41, 43)( 45, 46)( 48, 51)( 49, 53)( 50, 52)
( 54, 55)( 57, 60)( 58, 62)( 59, 61)( 63, 64)( 66, 69)( 67, 71)( 68, 70)
( 72, 73)( 75, 78)( 76, 80)( 77, 79)( 81, 82)( 84, 87)( 85, 89)( 86, 88)
( 90, 91)( 93, 96)( 94, 98)( 95, 97)( 99,100)(102,105)(103,107)(104,106)
(108,109)(111,114)(112,116)(113,115)(117,118)(120,123)(121,125)(122,124)
(126,127)(129,132)(130,134)(131,133)(135,136)(138,141)(139,143)(140,142)
(144,145);
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*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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