Polytope of Type {2,2,8,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,9}*1152
if this polytope has a name.
Group : SmallGroup(1152,155413)
Rank : 5
Schlafli Type : {2,2,8,9}
Number of vertices, edges, etc : 2, 2, 16, 72, 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 : {2,2,8,3}*384
4-fold quotients : {2,2,4,9}*288
6-fold quotients : {2,2,4,3}*192
8-fold quotients : {2,2,2,9}*144
12-fold quotients : {2,2,4,3}*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 := (3,4);;
s2 := ( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 83)( 10, 84)( 11, 82)( 12, 81)
( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 91)( 18, 92)( 19, 90)( 20, 89)
( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 99)( 26,100)( 27, 98)( 28, 97)
( 29,103)( 30,104)( 31,102)( 32,101)( 33,107)( 34,108)( 35,106)( 36,105)
( 37,111)( 38,112)( 39,110)( 40,109)( 41,115)( 42,116)( 43,114)( 44,113)
( 45,119)( 46,120)( 47,118)( 48,117)( 49,123)( 50,124)( 51,122)( 52,121)
( 53,127)( 54,128)( 55,126)( 56,125)( 57,131)( 58,132)( 59,130)( 60,129)
( 61,135)( 62,136)( 63,134)( 64,133)( 65,139)( 66,140)( 67,138)( 68,137)
( 69,143)( 70,144)( 71,142)( 72,141)( 73,147)( 74,148)( 75,146)( 76,145);;
s3 := ( 7, 9)( 8, 10)( 11, 12)( 13, 21)( 14, 22)( 15, 25)( 16, 26)( 17, 23)
( 18, 24)( 19, 28)( 20, 27)( 29, 61)( 30, 62)( 31, 65)( 32, 66)( 33, 63)
( 34, 64)( 35, 68)( 36, 67)( 37, 53)( 38, 54)( 39, 57)( 40, 58)( 41, 55)
( 42, 56)( 43, 60)( 44, 59)( 45, 69)( 46, 70)( 47, 73)( 48, 74)( 49, 71)
( 50, 72)( 51, 76)( 52, 75)( 77, 78)( 79, 82)( 80, 81)( 85, 94)( 86, 93)
( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 99)( 92,100)(101,134)(102,133)
(103,138)(104,137)(105,136)(106,135)(107,139)(108,140)(109,126)(110,125)
(111,130)(112,129)(113,128)(114,127)(115,131)(116,132)(117,142)(118,141)
(119,146)(120,145)(121,144)(122,143)(123,147)(124,148);;
s4 := ( 5, 29)( 6, 30)( 7, 32)( 8, 31)( 9, 35)( 10, 36)( 11, 33)( 12, 34)
( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)( 20, 50)
( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 43)( 26, 44)( 27, 41)( 28, 42)
( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 67)( 58, 68)( 59, 65)( 60, 66)
( 71, 72)( 73, 75)( 74, 76)( 77,102)( 78,101)( 79,103)( 80,104)( 81,108)
( 82,107)( 83,106)( 84,105)( 85,118)( 86,117)( 87,119)( 88,120)( 89,124)
( 90,123)( 91,122)( 92,121)( 93,110)( 94,109)( 95,111)( 96,112)( 97,116)
( 98,115)( 99,114)(100,113)(125,134)(126,133)(127,135)(128,136)(129,140)
(130,139)(131,138)(132,137)(141,142)(145,148)(146,147);;
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*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(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := Sym(148)!( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 83)( 10, 84)( 11, 82)
( 12, 81)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 91)( 18, 92)( 19, 90)
( 20, 89)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 99)( 26,100)( 27, 98)
( 28, 97)( 29,103)( 30,104)( 31,102)( 32,101)( 33,107)( 34,108)( 35,106)
( 36,105)( 37,111)( 38,112)( 39,110)( 40,109)( 41,115)( 42,116)( 43,114)
( 44,113)( 45,119)( 46,120)( 47,118)( 48,117)( 49,123)( 50,124)( 51,122)
( 52,121)( 53,127)( 54,128)( 55,126)( 56,125)( 57,131)( 58,132)( 59,130)
( 60,129)( 61,135)( 62,136)( 63,134)( 64,133)( 65,139)( 66,140)( 67,138)
( 68,137)( 69,143)( 70,144)( 71,142)( 72,141)( 73,147)( 74,148)( 75,146)
( 76,145);
s3 := Sym(148)!( 7, 9)( 8, 10)( 11, 12)( 13, 21)( 14, 22)( 15, 25)( 16, 26)
( 17, 23)( 18, 24)( 19, 28)( 20, 27)( 29, 61)( 30, 62)( 31, 65)( 32, 66)
( 33, 63)( 34, 64)( 35, 68)( 36, 67)( 37, 53)( 38, 54)( 39, 57)( 40, 58)
( 41, 55)( 42, 56)( 43, 60)( 44, 59)( 45, 69)( 46, 70)( 47, 73)( 48, 74)
( 49, 71)( 50, 72)( 51, 76)( 52, 75)( 77, 78)( 79, 82)( 80, 81)( 85, 94)
( 86, 93)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 99)( 92,100)(101,134)
(102,133)(103,138)(104,137)(105,136)(106,135)(107,139)(108,140)(109,126)
(110,125)(111,130)(112,129)(113,128)(114,127)(115,131)(116,132)(117,142)
(118,141)(119,146)(120,145)(121,144)(122,143)(123,147)(124,148);
s4 := Sym(148)!( 5, 29)( 6, 30)( 7, 32)( 8, 31)( 9, 35)( 10, 36)( 11, 33)
( 12, 34)( 13, 45)( 14, 46)( 15, 48)( 16, 47)( 17, 51)( 18, 52)( 19, 49)
( 20, 50)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 43)( 26, 44)( 27, 41)
( 28, 42)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 57, 67)( 58, 68)( 59, 65)
( 60, 66)( 71, 72)( 73, 75)( 74, 76)( 77,102)( 78,101)( 79,103)( 80,104)
( 81,108)( 82,107)( 83,106)( 84,105)( 85,118)( 86,117)( 87,119)( 88,120)
( 89,124)( 90,123)( 91,122)( 92,121)( 93,110)( 94,109)( 95,111)( 96,112)
( 97,116)( 98,115)( 99,114)(100,113)(125,134)(126,133)(127,135)(128,136)
(129,140)(130,139)(131,138)(132,137)(141,142)(145,148)(146,147);
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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope