Polytope of Type {2,4,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,18}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {2,4,18}
Number of vertices, edges, etc : 2, 16, 144, 72
Order of s0s1s2s3 : 36
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 : {2,4,18}*576
3-fold quotients : {2,4,6}*384b
4-fold quotients : {2,4,18}*288a, {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c
6-fold quotients : {2,4,6}*192
8-fold quotients : {2,4,9}*144, {2,2,18}*144
12-fold quotients : {2,4,6}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
16-fold quotients : {2,2,9}*72
24-fold quotients : {2,4,3}*48, {2,2,6}*48
36-fold quotients : {2,4,2}*32
48-fold quotients : {2,2,3}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75,113)( 76,114)( 77,111)( 78,112)
( 79,117)( 80,118)( 81,115)( 82,116)( 83,121)( 84,122)( 85,119)( 86,120)
( 87,125)( 88,126)( 89,123)( 90,124)( 91,129)( 92,130)( 93,127)( 94,128)
( 95,133)( 96,134)( 97,131)( 98,132)( 99,137)(100,138)(101,135)(102,136)
(103,141)(104,142)(105,139)(106,140)(107,145)(108,146)(109,143)(110,144);;
s2 := ( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 83)( 8, 85)( 9, 84)( 10, 86)
( 11, 79)( 12, 81)( 13, 80)( 14, 82)( 15,107)( 16,109)( 17,108)( 18,110)
( 19,103)( 20,105)( 21,104)( 22,106)( 23, 99)( 24,101)( 25,100)( 26,102)
( 27, 95)( 28, 97)( 29, 96)( 30, 98)( 31, 91)( 32, 93)( 33, 92)( 34, 94)
( 35, 87)( 36, 89)( 37, 88)( 38, 90)( 39,111)( 40,113)( 41,112)( 42,114)
( 43,119)( 44,121)( 45,120)( 46,122)( 47,115)( 48,117)( 49,116)( 50,118)
( 51,143)( 52,145)( 53,144)( 54,146)( 55,139)( 56,141)( 57,140)( 58,142)
( 59,135)( 60,137)( 61,136)( 62,138)( 63,131)( 64,133)( 65,132)( 66,134)
( 67,127)( 68,129)( 69,128)( 70,130)( 71,123)( 72,125)( 73,124)( 74,126);;
s3 := ( 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]);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75,113)( 76,114)( 77,111)
( 78,112)( 79,117)( 80,118)( 81,115)( 82,116)( 83,121)( 84,122)( 85,119)
( 86,120)( 87,125)( 88,126)( 89,123)( 90,124)( 91,129)( 92,130)( 93,127)
( 94,128)( 95,133)( 96,134)( 97,131)( 98,132)( 99,137)(100,138)(101,135)
(102,136)(103,141)(104,142)(105,139)(106,140)(107,145)(108,146)(109,143)
(110,144);
s2 := Sym(146)!( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 83)( 8, 85)( 9, 84)
( 10, 86)( 11, 79)( 12, 81)( 13, 80)( 14, 82)( 15,107)( 16,109)( 17,108)
( 18,110)( 19,103)( 20,105)( 21,104)( 22,106)( 23, 99)( 24,101)( 25,100)
( 26,102)( 27, 95)( 28, 97)( 29, 96)( 30, 98)( 31, 91)( 32, 93)( 33, 92)
( 34, 94)( 35, 87)( 36, 89)( 37, 88)( 38, 90)( 39,111)( 40,113)( 41,112)
( 42,114)( 43,119)( 44,121)( 45,120)( 46,122)( 47,115)( 48,117)( 49,116)
( 50,118)( 51,143)( 52,145)( 53,144)( 54,146)( 55,139)( 56,141)( 57,140)
( 58,142)( 59,135)( 60,137)( 61,136)( 62,138)( 63,131)( 64,133)( 65,132)
( 66,134)( 67,127)( 68,129)( 69,128)( 70,130)( 71,123)( 72,125)( 73,124)
( 74,126);
s3 := 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>;
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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*s2*s3*s2*s3 >;
to this polytope