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Polytope of Type {2,8,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,18}*1152c
if this polytope has a name.
Group : SmallGroup(1152,155421)
Rank : 4
Schlafli Type : {2,8,18}
Number of vertices, edges, etc : 2, 16, 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) :
   2-fold quotients : {2,4,18}*576
   3-fold quotients : {2,8,6}*384c
   4-fold quotients : {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c
   6-fold quotients : {2,4,6}*192
   8-fold quotients : {2,4,9}*144, {2,2,18}*144
   12-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,2,9}*72
   24-fold quotients : {2,4,3}*48, {2,2,6}*48
   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 := (  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)( 10, 78)
( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)( 18, 86)
( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)( 26, 94)
( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)( 34,102)
( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)( 42,110)
( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)( 50,118)
( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)( 58,126)
( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)( 66,134)
( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)( 74,142);;
s2 := (  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 26)( 18, 25)( 27, 67)( 28, 68)( 29, 72)( 30, 71)( 31, 70)
( 32, 69)( 33, 74)( 34, 73)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)
( 40, 61)( 41, 66)( 42, 65)( 43, 51)( 44, 52)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 58)( 50, 57)( 77, 80)( 78, 79)( 81, 82)( 83, 91)( 84, 92)
( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 98)( 90, 97)( 99,139)(100,140)
(101,144)(102,143)(103,142)(104,141)(105,146)(106,145)(107,131)(108,132)
(109,136)(110,135)(111,134)(112,133)(113,138)(114,137)(115,123)(116,124)
(117,128)(118,127)(119,126)(120,125)(121,130)(122,129);;
s3 := (  3, 51)(  4, 52)(  5, 57)(  6, 58)(  7, 56)(  8, 55)(  9, 53)( 10, 54)
( 11, 67)( 12, 68)( 13, 73)( 14, 74)( 15, 72)( 16, 71)( 17, 69)( 18, 70)
( 19, 59)( 20, 60)( 21, 65)( 22, 66)( 23, 64)( 24, 63)( 25, 61)( 26, 62)
( 29, 33)( 30, 34)( 31, 32)( 35, 43)( 36, 44)( 37, 49)( 38, 50)( 39, 48)
( 40, 47)( 41, 45)( 42, 46)( 75,124)( 76,123)( 77,130)( 78,129)( 79,127)
( 80,128)( 81,126)( 82,125)( 83,140)( 84,139)( 85,146)( 86,145)( 87,143)
( 88,144)( 89,142)( 90,141)( 91,132)( 92,131)( 93,138)( 94,137)( 95,135)
( 96,136)( 97,134)( 98,133)( 99,100)(101,106)(102,105)(107,116)(108,115)
(109,122)(110,121)(111,119)(112,120)(113,118)(114,117);;
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*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)!(  3, 79)(  4, 80)(  5, 82)(  6, 81)(  7, 76)(  8, 75)(  9, 77)
( 10, 78)( 11, 87)( 12, 88)( 13, 90)( 14, 89)( 15, 84)( 16, 83)( 17, 85)
( 18, 86)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)
( 26, 94)( 27,103)( 28,104)( 29,106)( 30,105)( 31,100)( 32, 99)( 33,101)
( 34,102)( 35,111)( 36,112)( 37,114)( 38,113)( 39,108)( 40,107)( 41,109)
( 42,110)( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)
( 50,118)( 51,127)( 52,128)( 53,130)( 54,129)( 55,124)( 56,123)( 57,125)
( 58,126)( 59,135)( 60,136)( 61,138)( 62,137)( 63,132)( 64,131)( 65,133)
( 66,134)( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)
( 74,142);
s2 := Sym(146)!(  5,  8)(  6,  7)(  9, 10)( 11, 19)( 12, 20)( 13, 24)( 14, 23)
( 15, 22)( 16, 21)( 17, 26)( 18, 25)( 27, 67)( 28, 68)( 29, 72)( 30, 71)
( 31, 70)( 32, 69)( 33, 74)( 34, 73)( 35, 59)( 36, 60)( 37, 64)( 38, 63)
( 39, 62)( 40, 61)( 41, 66)( 42, 65)( 43, 51)( 44, 52)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 58)( 50, 57)( 77, 80)( 78, 79)( 81, 82)( 83, 91)
( 84, 92)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 98)( 90, 97)( 99,139)
(100,140)(101,144)(102,143)(103,142)(104,141)(105,146)(106,145)(107,131)
(108,132)(109,136)(110,135)(111,134)(112,133)(113,138)(114,137)(115,123)
(116,124)(117,128)(118,127)(119,126)(120,125)(121,130)(122,129);
s3 := Sym(146)!(  3, 51)(  4, 52)(  5, 57)(  6, 58)(  7, 56)(  8, 55)(  9, 53)
( 10, 54)( 11, 67)( 12, 68)( 13, 73)( 14, 74)( 15, 72)( 16, 71)( 17, 69)
( 18, 70)( 19, 59)( 20, 60)( 21, 65)( 22, 66)( 23, 64)( 24, 63)( 25, 61)
( 26, 62)( 29, 33)( 30, 34)( 31, 32)( 35, 43)( 36, 44)( 37, 49)( 38, 50)
( 39, 48)( 40, 47)( 41, 45)( 42, 46)( 75,124)( 76,123)( 77,130)( 78,129)
( 79,127)( 80,128)( 81,126)( 82,125)( 83,140)( 84,139)( 85,146)( 86,145)
( 87,143)( 88,144)( 89,142)( 90,141)( 91,132)( 92,131)( 93,138)( 94,137)
( 95,135)( 96,136)( 97,134)( 98,133)( 99,100)(101,106)(102,105)(107,116)
(108,115)(109,122)(110,121)(111,119)(112,120)(113,118)(114,117);
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, s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*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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