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}*1152b
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}*384b
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, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)
( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)
( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)
( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)
(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)
(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)
(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148);;
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*s2*s3*s4*s2*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*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*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := Sym(148)!( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)
( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)
( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)
( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)
( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)
( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)
( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)
(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)
(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)
(147,148);
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*s2*s3*s4*s2*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*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*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope