Polytope of Type {2,4,4,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,9}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 5
Schlafli Type : {2,4,4,9}
Number of vertices, edges, etc : 2, 4, 16, 36, 18
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,4,9}*576
3-fold quotients : {2,4,4,3}*384b
4-fold quotients : {2,4,2,9}*288, {2,2,4,9}*288
6-fold quotients : {2,2,4,3}*192
8-fold quotients : {2,2,2,9}*144
12-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)
( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)
( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)( 98,134)
( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)(106,142)
(107,143)(108,144)(109,145)(110,146);;
s2 := ( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 81)( 8, 82)( 9, 79)( 10, 80)
( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)( 18, 88)
( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)( 26, 96)
( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)( 34,104)
( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)( 42,112)
( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)( 50,120)
( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)( 58,128)
( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)( 66,136)
( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)( 74,144);;
s3 := ( 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);;
s4 := ( 3, 27)( 4, 30)( 5, 29)( 6, 28)( 7, 35)( 8, 38)( 9, 37)( 10, 36)
( 11, 31)( 12, 34)( 13, 33)( 14, 32)( 16, 18)( 19, 23)( 20, 26)( 21, 25)
( 22, 24)( 39, 63)( 40, 66)( 41, 65)( 42, 64)( 43, 71)( 44, 74)( 45, 73)
( 46, 72)( 47, 67)( 48, 70)( 49, 69)( 50, 68)( 52, 54)( 55, 59)( 56, 62)
( 57, 61)( 58, 60)( 75, 99)( 76,102)( 77,101)( 78,100)( 79,107)( 80,110)
( 81,109)( 82,108)( 83,103)( 84,106)( 85,105)( 86,104)( 88, 90)( 91, 95)
( 92, 98)( 93, 97)( 94, 96)(111,135)(112,138)(113,137)(114,136)(115,143)
(116,146)(117,145)(118,144)(119,139)(120,142)(121,141)(122,140)(124,126)
(127,131)(128,134)(129,133)(130,132);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)
( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)
( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)
( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)
(106,142)(107,143)(108,144)(109,145)(110,146);
s2 := Sym(146)!( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 81)( 8, 82)( 9, 79)
( 10, 80)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)
( 18, 88)( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)
( 26, 96)( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)
( 34,104)( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)
( 42,112)( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)
( 50,120)( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)
( 58,128)( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)
( 66,136)( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)
( 74,144);
s3 := 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);
s4 := Sym(146)!( 3, 27)( 4, 30)( 5, 29)( 6, 28)( 7, 35)( 8, 38)( 9, 37)
( 10, 36)( 11, 31)( 12, 34)( 13, 33)( 14, 32)( 16, 18)( 19, 23)( 20, 26)
( 21, 25)( 22, 24)( 39, 63)( 40, 66)( 41, 65)( 42, 64)( 43, 71)( 44, 74)
( 45, 73)( 46, 72)( 47, 67)( 48, 70)( 49, 69)( 50, 68)( 52, 54)( 55, 59)
( 56, 62)( 57, 61)( 58, 60)( 75, 99)( 76,102)( 77,101)( 78,100)( 79,107)
( 80,110)( 81,109)( 82,108)( 83,103)( 84,106)( 85,105)( 86,104)( 88, 90)
( 91, 95)( 92, 98)( 93, 97)( 94, 96)(111,135)(112,138)(113,137)(114,136)
(115,143)(116,146)(117,145)(118,144)(119,139)(120,142)(121,141)(122,140)
(124,126)(127,131)(128,134)(129,133)(130,132);
poly := sub<Sym(146)|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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, 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 >;
to this polytope