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Polytope of Type {2,2,4,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,36}*1152c
if this polytope has a name.
Group : SmallGroup(1152,155400)
Rank : 5
Schlafli Type : {2,2,4,36}
Number of vertices, edges, etc : 2, 2, 4, 72, 36
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 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) :
   2-fold quotients : {2,2,4,18}*576b
   3-fold quotients : {2,2,4,12}*384c
   4-fold quotients : {2,2,4,9}*288
   6-fold quotients : {2,2,4,6}*192c
   12-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (  5, 42)(  6, 41)(  7, 44)(  8, 43)(  9, 46)( 10, 45)( 11, 48)( 12, 47)
( 13, 50)( 14, 49)( 15, 52)( 16, 51)( 17, 54)( 18, 53)( 19, 56)( 20, 55)
( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 62)( 26, 61)( 27, 64)( 28, 63)
( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 70)( 34, 69)( 35, 72)( 36, 71)
( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 77,114)( 78,113)( 79,116)( 80,115)
( 81,118)( 82,117)( 83,120)( 84,119)( 85,122)( 86,121)( 87,124)( 88,123)
( 89,126)( 90,125)( 91,128)( 92,127)( 93,130)( 94,129)( 95,132)( 96,131)
( 97,134)( 98,133)( 99,136)(100,135)(101,138)(102,137)(103,140)(104,139)
(105,142)(106,141)(107,144)(108,143)(109,146)(110,145)(111,148)(112,147);;
s3 := (  6,  7)(  9, 13)( 10, 15)( 11, 14)( 12, 16)( 17, 33)( 18, 35)( 19, 34)
( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 25, 37)( 26, 39)( 27, 38)
( 28, 40)( 42, 43)( 45, 49)( 46, 51)( 47, 50)( 48, 52)( 53, 69)( 54, 71)
( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 61, 73)( 62, 75)
( 63, 74)( 64, 76)( 77,113)( 78,115)( 79,114)( 80,116)( 81,121)( 82,123)
( 83,122)( 84,124)( 85,117)( 86,119)( 87,118)( 88,120)( 89,141)( 90,143)
( 91,142)( 92,144)( 93,137)( 94,139)( 95,138)( 96,140)( 97,145)( 98,147)
( 99,146)(100,148)(101,129)(102,131)(103,130)(104,132)(105,125)(106,127)
(107,126)(108,128)(109,133)(110,135)(111,134)(112,136);;
s4 := (  5, 89)(  6, 90)(  7, 92)(  8, 91)(  9, 97)( 10, 98)( 11,100)( 12, 99)
( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 77)( 18, 78)( 19, 80)( 20, 79)
( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 81)( 26, 82)( 27, 84)( 28, 83)
( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)
( 37,109)( 38,110)( 39,112)( 40,111)( 41,125)( 42,126)( 43,128)( 44,127)
( 45,133)( 46,134)( 47,136)( 48,135)( 49,129)( 50,130)( 51,132)( 52,131)
( 53,113)( 54,114)( 55,116)( 56,115)( 57,121)( 58,122)( 59,124)( 60,123)
( 61,117)( 62,118)( 63,120)( 64,119)( 65,141)( 66,142)( 67,144)( 68,143)
( 69,137)( 70,138)( 71,140)( 72,139)( 73,145)( 74,146)( 75,148)( 76,147);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := Sym(148)!(  5, 42)(  6, 41)(  7, 44)(  8, 43)(  9, 46)( 10, 45)( 11, 48)
( 12, 47)( 13, 50)( 14, 49)( 15, 52)( 16, 51)( 17, 54)( 18, 53)( 19, 56)
( 20, 55)( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 62)( 26, 61)( 27, 64)
( 28, 63)( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 70)( 34, 69)( 35, 72)
( 36, 71)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 77,114)( 78,113)( 79,116)
( 80,115)( 81,118)( 82,117)( 83,120)( 84,119)( 85,122)( 86,121)( 87,124)
( 88,123)( 89,126)( 90,125)( 91,128)( 92,127)( 93,130)( 94,129)( 95,132)
( 96,131)( 97,134)( 98,133)( 99,136)(100,135)(101,138)(102,137)(103,140)
(104,139)(105,142)(106,141)(107,144)(108,143)(109,146)(110,145)(111,148)
(112,147);
s3 := Sym(148)!(  6,  7)(  9, 13)( 10, 15)( 11, 14)( 12, 16)( 17, 33)( 18, 35)
( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 25, 37)( 26, 39)
( 27, 38)( 28, 40)( 42, 43)( 45, 49)( 46, 51)( 47, 50)( 48, 52)( 53, 69)
( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 61, 73)
( 62, 75)( 63, 74)( 64, 76)( 77,113)( 78,115)( 79,114)( 80,116)( 81,121)
( 82,123)( 83,122)( 84,124)( 85,117)( 86,119)( 87,118)( 88,120)( 89,141)
( 90,143)( 91,142)( 92,144)( 93,137)( 94,139)( 95,138)( 96,140)( 97,145)
( 98,147)( 99,146)(100,148)(101,129)(102,131)(103,130)(104,132)(105,125)
(106,127)(107,126)(108,128)(109,133)(110,135)(111,134)(112,136);
s4 := Sym(148)!(  5, 89)(  6, 90)(  7, 92)(  8, 91)(  9, 97)( 10, 98)( 11,100)
( 12, 99)( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 77)( 18, 78)( 19, 80)
( 20, 79)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 81)( 26, 82)( 27, 84)
( 28, 83)( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)
( 36,103)( 37,109)( 38,110)( 39,112)( 40,111)( 41,125)( 42,126)( 43,128)
( 44,127)( 45,133)( 46,134)( 47,136)( 48,135)( 49,129)( 50,130)( 51,132)
( 52,131)( 53,113)( 54,114)( 55,116)( 56,115)( 57,121)( 58,122)( 59,124)
( 60,123)( 61,117)( 62,118)( 63,120)( 64,119)( 65,141)( 66,142)( 67,144)
( 68,143)( 69,137)( 70,138)( 71,140)( 72,139)( 73,145)( 74,146)( 75,148)
( 76,147);
poly := sub<Sym(148)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4 >; 
 

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