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Polytope of Type {8,18,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18,2}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 4
Schlafli Type : {8,18,2}
Number of vertices, edges, etc : 16, 144, 36, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {8,6,2}*384a
   4-fold quotients : {4,18,2}*288c
   8-fold quotients : {4,9,2}*144
   12-fold quotients : {4,6,2}*96b
   24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 32)( 22, 31)( 23, 30)( 24, 29)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)( 40, 45)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 64)( 54, 63)( 55, 62)( 56, 61)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 80)( 70, 79)( 71, 78)( 72, 77)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 96)( 86, 95)( 87, 94)( 88, 93)
( 97,105)( 98,106)( 99,107)(100,108)(101,112)(102,111)(103,110)(104,109)
(113,121)(114,122)(115,123)(116,124)(117,128)(118,127)(119,126)(120,125)
(129,137)(130,138)(131,139)(132,140)(133,144)(134,143)(135,142)(136,141);;
s1 := (  3,  4)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 15, 16)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 38)( 26, 37)
( 27, 39)( 28, 40)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)( 50,114)
( 51,116)( 52,115)( 53,122)( 54,121)( 55,123)( 56,124)( 57,118)( 58,117)
( 59,119)( 60,120)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)( 66, 98)
( 67,100)( 68, 99)( 69,106)( 70,105)( 71,107)( 72,108)( 73,102)( 74,101)
( 75,103)( 76,104)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,138)( 86,137)( 87,139)( 88,140)( 89,134)( 90,133)
( 91,135)( 92,136)( 93,141)( 94,142)( 95,144)( 96,143);;
s2 := (  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,110)(  6,111)(  7,112)(  8,109)
(  9,105)( 10,108)( 11,107)( 12,106)( 13,104)( 14,101)( 15,102)( 16,103)
( 17,129)( 18,132)( 19,131)( 20,130)( 21,142)( 22,143)( 23,144)( 24,141)
( 25,137)( 26,140)( 27,139)( 28,138)( 29,136)( 30,133)( 31,134)( 32,135)
( 33,113)( 34,116)( 35,115)( 36,114)( 37,126)( 38,127)( 39,128)( 40,125)
( 41,121)( 42,124)( 43,123)( 44,122)( 45,120)( 46,117)( 47,118)( 48,119)
( 50, 52)( 53, 62)( 54, 63)( 55, 64)( 56, 61)( 58, 60)( 65, 81)( 66, 84)
( 67, 83)( 68, 82)( 69, 94)( 70, 95)( 71, 96)( 72, 93)( 73, 89)( 74, 92)
( 75, 91)( 76, 90)( 77, 88)( 78, 85)( 79, 86)( 80, 87);;
s3 := (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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 16)(  6, 15)(  7, 14)
(  8, 13)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 32)( 22, 31)( 23, 30)
( 24, 29)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 48)( 38, 47)( 39, 46)
( 40, 45)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 64)( 54, 63)( 55, 62)
( 56, 61)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 80)( 70, 79)( 71, 78)
( 72, 77)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 96)( 86, 95)( 87, 94)
( 88, 93)( 97,105)( 98,106)( 99,107)(100,108)(101,112)(102,111)(103,110)
(104,109)(113,121)(114,122)(115,123)(116,124)(117,128)(118,127)(119,126)
(120,125)(129,137)(130,138)(131,139)(132,140)(133,144)(134,143)(135,142)
(136,141);
s1 := Sym(146)!(  3,  4)(  5, 10)(  6,  9)(  7, 11)(  8, 12)( 15, 16)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 38)
( 26, 37)( 27, 39)( 28, 40)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)
( 50,114)( 51,116)( 52,115)( 53,122)( 54,121)( 55,123)( 56,124)( 57,118)
( 58,117)( 59,119)( 60,120)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)
( 66, 98)( 67,100)( 68, 99)( 69,106)( 70,105)( 71,107)( 72,108)( 73,102)
( 74,101)( 75,103)( 76,104)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)
( 82,130)( 83,132)( 84,131)( 85,138)( 86,137)( 87,139)( 88,140)( 89,134)
( 90,133)( 91,135)( 92,136)( 93,141)( 94,142)( 95,144)( 96,143);
s2 := Sym(146)!(  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,110)(  6,111)(  7,112)
(  8,109)(  9,105)( 10,108)( 11,107)( 12,106)( 13,104)( 14,101)( 15,102)
( 16,103)( 17,129)( 18,132)( 19,131)( 20,130)( 21,142)( 22,143)( 23,144)
( 24,141)( 25,137)( 26,140)( 27,139)( 28,138)( 29,136)( 30,133)( 31,134)
( 32,135)( 33,113)( 34,116)( 35,115)( 36,114)( 37,126)( 38,127)( 39,128)
( 40,125)( 41,121)( 42,124)( 43,123)( 44,122)( 45,120)( 46,117)( 47,118)
( 48,119)( 50, 52)( 53, 62)( 54, 63)( 55, 64)( 56, 61)( 58, 60)( 65, 81)
( 66, 84)( 67, 83)( 68, 82)( 69, 94)( 70, 95)( 71, 96)( 72, 93)( 73, 89)
( 74, 92)( 75, 91)( 76, 90)( 77, 88)( 78, 85)( 79, 86)( 80, 87);
s3 := Sym(146)!(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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 >; 
 

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