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Polytope of Type {2,18,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,155421)
Rank : 4
Schlafli Type : {2,18,8}
Number of vertices, edges, etc : 2, 36, 144, 16
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 : {2,18,4}*576
   3-fold quotients : {2,6,8}*384c
   4-fold quotients : {2,9,4}*288, {2,18,4}*288b, {2,18,4}*288c
   6-fold quotients : {2,6,4}*192
   8-fold quotients : {2,9,4}*144, {2,18,2}*144
   12-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,9,2}*72
   24-fold quotients : {2,3,4}*48, {2,6,2}*48
   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 := (  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)( 75, 76)( 77, 79)( 78, 80)( 83, 92)( 84, 91)
( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,140)(100,139)
(101,143)(102,144)(103,141)(104,142)(105,145)(106,146)(107,132)(108,131)
(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,124)(116,123)
(117,127)(118,128)(119,125)(120,126)(121,129)(122,130);;
s2 := (  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 33)(  8, 34)(  9, 31)( 10, 32)
( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)
( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)( 26, 40)
( 51, 67)( 52, 68)( 53, 70)( 54, 69)( 55, 73)( 56, 74)( 57, 71)( 58, 72)
( 61, 62)( 63, 65)( 64, 66)( 75, 99)( 76,100)( 77,102)( 78,101)( 79,105)
( 80,106)( 81,103)( 82,104)( 83,115)( 84,116)( 85,118)( 86,117)( 87,121)
( 88,122)( 89,119)( 90,120)( 91,107)( 92,108)( 93,110)( 94,109)( 95,113)
( 96,114)( 97,111)( 98,112)(123,139)(124,140)(125,142)(126,141)(127,145)
(128,146)(129,143)(130,144)(133,134)(135,137)(136,138);;
s3 := (  3, 81)(  4, 82)(  5, 79)(  6, 80)(  7, 78)(  8, 77)(  9, 76)( 10, 75)
( 11, 89)( 12, 90)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 84)( 18, 83)
( 19, 97)( 20, 98)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 92)( 26, 91)
( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)( 34, 99)
( 35,113)( 36,114)( 37,111)( 38,112)( 39,110)( 40,109)( 41,108)( 42,107)
( 43,121)( 44,122)( 45,119)( 46,120)( 47,118)( 48,117)( 49,116)( 50,115)
( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)( 58,123)
( 59,137)( 60,138)( 61,135)( 62,136)( 63,134)( 64,133)( 65,132)( 66,131)
( 67,145)( 68,146)( 69,143)( 70,144)( 71,142)( 72,141)( 73,140)( 74,139);;
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*s3*s1*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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := 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)( 75, 76)( 77, 79)( 78, 80)( 83, 92)
( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 89, 97)( 90, 98)( 99,140)
(100,139)(101,143)(102,144)(103,141)(104,142)(105,145)(106,146)(107,132)
(108,131)(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,124)
(116,123)(117,127)(118,128)(119,125)(120,126)(121,129)(122,130);
s2 := Sym(146)!(  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 33)(  8, 34)(  9, 31)
( 10, 32)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)
( 18, 48)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)
( 26, 40)( 51, 67)( 52, 68)( 53, 70)( 54, 69)( 55, 73)( 56, 74)( 57, 71)
( 58, 72)( 61, 62)( 63, 65)( 64, 66)( 75, 99)( 76,100)( 77,102)( 78,101)
( 79,105)( 80,106)( 81,103)( 82,104)( 83,115)( 84,116)( 85,118)( 86,117)
( 87,121)( 88,122)( 89,119)( 90,120)( 91,107)( 92,108)( 93,110)( 94,109)
( 95,113)( 96,114)( 97,111)( 98,112)(123,139)(124,140)(125,142)(126,141)
(127,145)(128,146)(129,143)(130,144)(133,134)(135,137)(136,138);
s3 := Sym(146)!(  3, 81)(  4, 82)(  5, 79)(  6, 80)(  7, 78)(  8, 77)(  9, 76)
( 10, 75)( 11, 89)( 12, 90)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 84)
( 18, 83)( 19, 97)( 20, 98)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 92)
( 26, 91)( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)
( 34, 99)( 35,113)( 36,114)( 37,111)( 38,112)( 39,110)( 40,109)( 41,108)
( 42,107)( 43,121)( 44,122)( 45,119)( 46,120)( 47,118)( 48,117)( 49,116)
( 50,115)( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)
( 58,123)( 59,137)( 60,138)( 61,135)( 62,136)( 63,134)( 64,133)( 65,132)
( 66,131)( 67,145)( 68,146)( 69,143)( 70,144)( 71,142)( 72,141)( 73,140)
( 74,139);
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*s3*s1*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*s1*s2*s1*s2*s1*s2 >; 
 

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