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Polytope of Type {2,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {2,18,4}
Number of vertices, edges, etc : 2, 72, 144, 16
Order of s0s1s2s3 : 36
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 : {2,6,4}*384b
   4-fold quotients : {2,18,4}*288a, {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 : {2,6,4}*96a, {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
   36-fold quotients : {2,2,4}*32
   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 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 35)( 16, 37)( 17, 36)
( 18, 38)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 27)( 24, 29)( 25, 28)
( 26, 30)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 71)( 52, 73)
( 53, 72)( 54, 74)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 63)( 60, 65)
( 61, 64)( 62, 66)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87,107)
( 88,109)( 89,108)( 90,110)( 91,103)( 92,105)( 93,104)( 94,106)( 95, 99)
( 96,101)( 97,100)( 98,102)(112,113)(115,119)(116,121)(117,120)(118,122)
(123,143)(124,145)(125,144)(126,146)(127,139)(128,141)(129,140)(130,142)
(131,135)(132,137)(133,136)(134,138);;
s2 := (  3, 15)(  4, 16)(  5, 18)(  6, 17)(  7, 23)(  8, 24)(  9, 26)( 10, 25)
( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 27, 35)( 28, 36)( 29, 38)( 30, 37)
( 33, 34)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)( 45, 62)
( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 63, 71)( 64, 72)( 65, 74)
( 66, 73)( 69, 70)( 75,123)( 76,124)( 77,126)( 78,125)( 79,131)( 80,132)
( 81,134)( 82,133)( 83,127)( 84,128)( 85,130)( 86,129)( 87,111)( 88,112)
( 89,114)( 90,113)( 91,119)( 92,120)( 93,122)( 94,121)( 95,115)( 96,116)
( 97,118)( 98,117)( 99,143)(100,144)(101,146)(102,145)(103,139)(104,140)
(105,142)(106,141)(107,135)(108,136)(109,138)(110,137);;
s3 := (  3, 78)(  4, 77)(  5, 76)(  6, 75)(  7, 82)(  8, 81)(  9, 80)( 10, 79)
( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 90)( 16, 89)( 17, 88)( 18, 87)
( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 98)( 24, 97)( 25, 96)( 26, 95)
( 27,102)( 28,101)( 29,100)( 30, 99)( 31,106)( 32,105)( 33,104)( 34,103)
( 35,110)( 36,109)( 37,108)( 38,107)( 39,114)( 40,113)( 41,112)( 42,111)
( 43,118)( 44,117)( 45,116)( 46,115)( 47,122)( 48,121)( 49,120)( 50,119)
( 51,126)( 52,125)( 53,124)( 54,123)( 55,130)( 56,129)( 57,128)( 58,127)
( 59,134)( 60,133)( 61,132)( 62,131)( 63,138)( 64,137)( 65,136)( 66,135)
( 67,142)( 68,141)( 69,140)( 70,139)( 71,146)( 72,145)( 73,144)( 74,143);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*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*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 15, 35)( 16, 37)
( 17, 36)( 18, 38)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 27)( 24, 29)
( 25, 28)( 26, 30)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 71)
( 52, 73)( 53, 72)( 54, 74)( 55, 67)( 56, 69)( 57, 68)( 58, 70)( 59, 63)
( 60, 65)( 61, 64)( 62, 66)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)
( 87,107)( 88,109)( 89,108)( 90,110)( 91,103)( 92,105)( 93,104)( 94,106)
( 95, 99)( 96,101)( 97,100)( 98,102)(112,113)(115,119)(116,121)(117,120)
(118,122)(123,143)(124,145)(125,144)(126,146)(127,139)(128,141)(129,140)
(130,142)(131,135)(132,137)(133,136)(134,138);
s2 := Sym(146)!(  3, 15)(  4, 16)(  5, 18)(  6, 17)(  7, 23)(  8, 24)(  9, 26)
( 10, 25)( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 27, 35)( 28, 36)( 29, 38)
( 30, 37)( 33, 34)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)
( 45, 62)( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 63, 71)( 64, 72)
( 65, 74)( 66, 73)( 69, 70)( 75,123)( 76,124)( 77,126)( 78,125)( 79,131)
( 80,132)( 81,134)( 82,133)( 83,127)( 84,128)( 85,130)( 86,129)( 87,111)
( 88,112)( 89,114)( 90,113)( 91,119)( 92,120)( 93,122)( 94,121)( 95,115)
( 96,116)( 97,118)( 98,117)( 99,143)(100,144)(101,146)(102,145)(103,139)
(104,140)(105,142)(106,141)(107,135)(108,136)(109,138)(110,137);
s3 := Sym(146)!(  3, 78)(  4, 77)(  5, 76)(  6, 75)(  7, 82)(  8, 81)(  9, 80)
( 10, 79)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 90)( 16, 89)( 17, 88)
( 18, 87)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 98)( 24, 97)( 25, 96)
( 26, 95)( 27,102)( 28,101)( 29,100)( 30, 99)( 31,106)( 32,105)( 33,104)
( 34,103)( 35,110)( 36,109)( 37,108)( 38,107)( 39,114)( 40,113)( 41,112)
( 42,111)( 43,118)( 44,117)( 45,116)( 46,115)( 47,122)( 48,121)( 49,120)
( 50,119)( 51,126)( 52,125)( 53,124)( 54,123)( 55,130)( 56,129)( 57,128)
( 58,127)( 59,134)( 60,133)( 61,132)( 62,131)( 63,138)( 64,137)( 65,136)
( 66,135)( 67,142)( 68,141)( 69,140)( 70,139)( 71,146)( 72,145)( 73,144)
( 74,143);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*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*s1*s2 >; 
 

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