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Polytope of Type {2,8,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,36}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97523)
Rank : 4
Schlafli Type : {2,8,36}
Number of vertices, edges, etc : 2, 8, 144, 36
Order of s0s1s2s3 : 72
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 : {2,4,36}*576a, {2,8,18}*576
   3-fold quotients : {2,8,12}*384a
   4-fold quotients : {2,2,36}*288, {2,4,18}*288a
   6-fold quotients : {2,4,12}*192a, {2,8,6}*192
   8-fold quotients : {2,2,18}*144
   9-fold quotients : {2,8,4}*128a
   12-fold quotients : {2,2,12}*96, {2,4,6}*96a
   16-fold quotients : {2,2,9}*72
   18-fold quotients : {2,4,4}*64, {2,8,2}*64
   24-fold quotients : {2,2,6}*48
   36-fold quotients : {2,2,4}*32, {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)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)( 63, 72)
( 64, 73)( 65, 74)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)
( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)
( 89,107)( 90,108)( 91,109)( 92,110)(111,129)(112,130)(113,131)(114,132)
(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)
(123,141)(124,142)(125,143)(126,144)(127,145)(128,146);;
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)( 39,111)( 40,113)( 41,112)( 42,118)
( 43,117)( 44,119)( 45,115)( 46,114)( 47,116)( 48,120)( 49,122)( 50,121)
( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,138)( 58,140)
( 59,139)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)( 66,129)
( 67,131)( 68,130)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)( 74,134);;
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)
( 75,114)( 76,116)( 77,115)( 78,111)( 79,113)( 80,112)( 81,118)( 82,117)
( 83,119)( 84,123)( 85,125)( 86,124)( 87,120)( 88,122)( 89,121)( 90,127)
( 91,126)( 92,128)( 93,132)( 94,134)( 95,133)( 96,129)( 97,131)( 98,130)
( 99,136)(100,135)(101,137)(102,141)(103,143)(104,142)(105,138)(106,140)
(107,139)(108,145)(109,144)(110,146);;
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*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, 
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*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)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)( 62, 71)
( 63, 72)( 64, 73)( 65, 74)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)
( 80, 98)( 81, 99)( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)
( 88,106)( 89,107)( 90,108)( 91,109)( 92,110)(111,129)(112,130)(113,131)
(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)
(122,140)(123,141)(124,142)(125,143)(126,144)(127,145)(128,146);
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)( 39,111)( 40,113)( 41,112)
( 42,118)( 43,117)( 44,119)( 45,115)( 46,114)( 47,116)( 48,120)( 49,122)
( 50,121)( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,138)
( 58,140)( 59,139)( 60,145)( 61,144)( 62,146)( 63,142)( 64,141)( 65,143)
( 66,129)( 67,131)( 68,130)( 69,136)( 70,135)( 71,137)( 72,133)( 73,132)
( 74,134);
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)( 75,114)( 76,116)( 77,115)( 78,111)( 79,113)( 80,112)( 81,118)
( 82,117)( 83,119)( 84,123)( 85,125)( 86,124)( 87,120)( 88,122)( 89,121)
( 90,127)( 91,126)( 92,128)( 93,132)( 94,134)( 95,133)( 96,129)( 97,131)
( 98,130)( 99,136)(100,135)(101,137)(102,141)(103,143)(104,142)(105,138)
(106,140)(107,139)(108,145)(109,144)(110,146);
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*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, 
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*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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