Polytope of Type {2,2,4,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,18}*1152
if this polytope has a name.
Group : SmallGroup(1152,157448)
Rank : 5
Schlafli Type : {2,2,4,18}
Number of vertices, edges, etc : 2, 2, 8, 72, 36
Order of s0s1s2s3s4 : 18
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, {2,2,4,18}*576b, {2,2,4,18}*576c
3-fold quotients : {2,2,4,6}*384
4-fold quotients : {2,2,4,9}*288, {2,2,2,18}*288
6-fold quotients : {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
8-fold quotients : {2,2,2,9}*144
12-fold quotients : {2,2,4,3}*96, {2,2,2,6}*96
24-fold quotients : {2,2,2,3}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 42)( 6, 41)( 7, 44)( 8, 43)( 9, 46)( 10, 45)( 11, 48)( 12, 47)
( 13, 50)( 14, 49)( 15, 52)( 16, 51)( 17, 54)( 18, 53)( 19, 56)( 20, 55)
( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 62)( 26, 61)( 27, 64)( 28, 63)
( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 70)( 34, 69)( 35, 72)( 36, 71)
( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 77,114)( 78,113)( 79,116)( 80,115)
( 81,118)( 82,117)( 83,120)( 84,119)( 85,122)( 86,121)( 87,124)( 88,123)
( 89,126)( 90,125)( 91,128)( 92,127)( 93,130)( 94,129)( 95,132)( 96,131)
( 97,134)( 98,133)( 99,136)(100,135)(101,138)(102,137)(103,140)(104,139)
(105,142)(106,141)(107,144)(108,143)(109,146)(110,145)(111,148)(112,147);;
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)( 78, 79)( 81, 85)( 82, 87)( 83, 86)( 84, 88)( 89,105)
( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)( 97,109)
( 98,111)( 99,110)(100,112)(114,115)(117,121)(118,123)(119,122)(120,124)
(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)(132,140)
(133,145)(134,147)(135,146)(136,148);;
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*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*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, 42)( 6, 41)( 7, 44)( 8, 43)( 9, 46)( 10, 45)( 11, 48)
( 12, 47)( 13, 50)( 14, 49)( 15, 52)( 16, 51)( 17, 54)( 18, 53)( 19, 56)
( 20, 55)( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 62)( 26, 61)( 27, 64)
( 28, 63)( 29, 66)( 30, 65)( 31, 68)( 32, 67)( 33, 70)( 34, 69)( 35, 72)
( 36, 71)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 77,114)( 78,113)( 79,116)
( 80,115)( 81,118)( 82,117)( 83,120)( 84,119)( 85,122)( 86,121)( 87,124)
( 88,123)( 89,126)( 90,125)( 91,128)( 92,127)( 93,130)( 94,129)( 95,132)
( 96,131)( 97,134)( 98,133)( 99,136)(100,135)(101,138)(102,137)(103,140)
(104,139)(105,142)(106,141)(107,144)(108,143)(109,146)(110,145)(111,148)
(112,147);
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)( 78, 79)( 81, 85)( 82, 87)( 83, 86)( 84, 88)
( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)( 94,103)( 95,102)( 96,104)
( 97,109)( 98,111)( 99,110)(100,112)(114,115)(117,121)(118,123)(119,122)
(120,124)(125,141)(126,143)(127,142)(128,144)(129,137)(130,139)(131,138)
(132,140)(133,145)(134,147)(135,146)(136,148);
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*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope