Polytope of Type {2,18,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,133439)
Rank : 4
Schlafli Type : {2,18,16}
Number of vertices, edges, etc : 2, 18, 144, 16
Order of s0s1s2s3 : 144
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 : {2,18,8}*576
3-fold quotients : {2,6,16}*384
4-fold quotients : {2,18,4}*288a
6-fold quotients : {2,6,8}*192
8-fold quotients : {2,18,2}*144
9-fold quotients : {2,2,16}*128
12-fold quotients : {2,6,4}*96a
16-fold quotients : {2,9,2}*72
18-fold quotients : {2,2,8}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 10)( 7, 9)( 8, 11)( 13, 14)( 15, 19)( 16, 18)( 17, 20)
( 22, 23)( 24, 28)( 25, 27)( 26, 29)( 31, 32)( 33, 37)( 34, 36)( 35, 38)
( 40, 41)( 42, 46)( 43, 45)( 44, 47)( 49, 50)( 51, 55)( 52, 54)( 53, 56)
( 58, 59)( 60, 64)( 61, 63)( 62, 65)( 67, 68)( 69, 73)( 70, 72)( 71, 74)
( 76, 77)( 78, 82)( 79, 81)( 80, 83)( 85, 86)( 87, 91)( 88, 90)( 89, 92)
( 94, 95)( 96,100)( 97, 99)( 98,101)(103,104)(105,109)(106,108)(107,110)
(112,113)(114,118)(115,117)(116,119)(121,122)(123,127)(124,126)(125,128)
(130,131)(132,136)(133,135)(134,137)(139,140)(141,145)(142,144)(143,146);;
s2 := ( 3, 6)( 4, 8)( 5, 7)( 9, 10)( 12, 15)( 13, 17)( 14, 16)( 18, 19)
( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 37)( 28, 36)
( 29, 38)( 39, 60)( 40, 62)( 41, 61)( 42, 57)( 43, 59)( 44, 58)( 45, 64)
( 46, 63)( 47, 65)( 48, 69)( 49, 71)( 50, 70)( 51, 66)( 52, 68)( 53, 67)
( 54, 73)( 55, 72)( 56, 74)( 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)( 93,141)( 94,143)( 95,142)
( 96,138)( 97,140)( 98,139)( 99,145)(100,144)(101,146)(102,132)(103,134)
(104,133)(105,129)(106,131)(107,130)(108,136)(109,135)(110,137);;
s3 := ( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)( 26,107)
( 27,108)( 28,109)( 29,110)( 30, 93)( 31, 94)( 32, 95)( 33, 96)( 34, 97)
( 35, 98)( 36, 99)( 37,100)( 38,101)( 39,129)( 40,130)( 41,131)( 42,132)
( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)
( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,111)( 58,112)
( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,118)( 65,119)( 66,120)
( 67,121)( 68,122)( 69,123)( 70,124)( 71,125)( 72,126)( 73,127)( 74,128);;
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, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 4, 5)( 6, 10)( 7, 9)( 8, 11)( 13, 14)( 15, 19)( 16, 18)
( 17, 20)( 22, 23)( 24, 28)( 25, 27)( 26, 29)( 31, 32)( 33, 37)( 34, 36)
( 35, 38)( 40, 41)( 42, 46)( 43, 45)( 44, 47)( 49, 50)( 51, 55)( 52, 54)
( 53, 56)( 58, 59)( 60, 64)( 61, 63)( 62, 65)( 67, 68)( 69, 73)( 70, 72)
( 71, 74)( 76, 77)( 78, 82)( 79, 81)( 80, 83)( 85, 86)( 87, 91)( 88, 90)
( 89, 92)( 94, 95)( 96,100)( 97, 99)( 98,101)(103,104)(105,109)(106,108)
(107,110)(112,113)(114,118)(115,117)(116,119)(121,122)(123,127)(124,126)
(125,128)(130,131)(132,136)(133,135)(134,137)(139,140)(141,145)(142,144)
(143,146);
s2 := Sym(146)!( 3, 6)( 4, 8)( 5, 7)( 9, 10)( 12, 15)( 13, 17)( 14, 16)
( 18, 19)( 21, 33)( 22, 35)( 23, 34)( 24, 30)( 25, 32)( 26, 31)( 27, 37)
( 28, 36)( 29, 38)( 39, 60)( 40, 62)( 41, 61)( 42, 57)( 43, 59)( 44, 58)
( 45, 64)( 46, 63)( 47, 65)( 48, 69)( 49, 71)( 50, 70)( 51, 66)( 52, 68)
( 53, 67)( 54, 73)( 55, 72)( 56, 74)( 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)( 93,141)( 94,143)
( 95,142)( 96,138)( 97,140)( 98,139)( 99,145)(100,144)(101,146)(102,132)
(103,134)(104,133)(105,129)(106,131)(107,130)(108,136)(109,135)(110,137);
s3 := Sym(146)!( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)
( 26,107)( 27,108)( 28,109)( 29,110)( 30, 93)( 31, 94)( 32, 95)( 33, 96)
( 34, 97)( 35, 98)( 36, 99)( 37,100)( 38,101)( 39,129)( 40,130)( 41,131)
( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)
( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,111)
( 58,112)( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,118)( 65,119)
( 66,120)( 67,121)( 68,122)( 69,123)( 70,124)( 71,125)( 72,126)( 73,127)
( 74,128);
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,
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope