Polytope of Type {2,2,18,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,157448)
Rank : 5
Schlafli Type : {2,2,18,4}
Number of vertices, edges, etc : 2, 2, 36, 72, 8
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 : {2,2,9,4}*576, {2,2,18,4}*576b, {2,2,18,4}*576c
3-fold quotients : {2,2,6,4}*384
4-fold quotients : {2,2,9,4}*288, {2,2,18,2}*288
6-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
8-fold quotients : {2,2,9,2}*144
12-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
24-fold quotients : {2,2,3,2}*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 := ( 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);;
s3 := ( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 61)( 10, 62)( 11, 64)( 12, 63)
( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 41)( 18, 42)( 19, 44)( 20, 43)
( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)( 28, 47)
( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 65)( 34, 66)( 35, 68)( 36, 67)
( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 77,125)( 78,126)( 79,128)( 80,127)
( 81,133)( 82,134)( 83,136)( 84,135)( 85,129)( 86,130)( 87,132)( 88,131)
( 89,113)( 90,114)( 91,116)( 92,115)( 93,121)( 94,122)( 95,124)( 96,123)
( 97,117)( 98,118)( 99,120)(100,119)(101,141)(102,142)(103,144)(104,143)
(105,137)(106,138)(107,140)(108,139)(109,145)(110,146)(111,148)(112,147);;
s4 := ( 5, 80)( 6, 79)( 7, 78)( 8, 77)( 9, 84)( 10, 83)( 11, 82)( 12, 81)
( 13, 88)( 14, 87)( 15, 86)( 16, 85)( 17, 92)( 18, 91)( 19, 90)( 20, 89)
( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25,100)( 26, 99)( 27, 98)( 28, 97)
( 29,104)( 30,103)( 31,102)( 32,101)( 33,108)( 34,107)( 35,106)( 36,105)
( 37,112)( 38,111)( 39,110)( 40,109)( 41,116)( 42,115)( 43,114)( 44,113)
( 45,120)( 46,119)( 47,118)( 48,117)( 49,124)( 50,123)( 51,122)( 52,121)
( 53,128)( 54,127)( 55,126)( 56,125)( 57,132)( 58,131)( 59,130)( 60,129)
( 61,136)( 62,135)( 63,134)( 64,133)( 65,140)( 66,139)( 67,138)( 68,137)
( 69,144)( 70,143)( 71,142)( 72,141)( 73,148)( 74,147)( 75,146)( 76,145);;
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, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(148)!(1,2);
s1 := Sym(148)!(3,4);
s2 := 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);
s3 := Sym(148)!( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 61)( 10, 62)( 11, 64)
( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 41)( 18, 42)( 19, 44)
( 20, 43)( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)
( 28, 47)( 29, 69)( 30, 70)( 31, 72)( 32, 71)( 33, 65)( 34, 66)( 35, 68)
( 36, 67)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 77,125)( 78,126)( 79,128)
( 80,127)( 81,133)( 82,134)( 83,136)( 84,135)( 85,129)( 86,130)( 87,132)
( 88,131)( 89,113)( 90,114)( 91,116)( 92,115)( 93,121)( 94,122)( 95,124)
( 96,123)( 97,117)( 98,118)( 99,120)(100,119)(101,141)(102,142)(103,144)
(104,143)(105,137)(106,138)(107,140)(108,139)(109,145)(110,146)(111,148)
(112,147);
s4 := Sym(148)!( 5, 80)( 6, 79)( 7, 78)( 8, 77)( 9, 84)( 10, 83)( 11, 82)
( 12, 81)( 13, 88)( 14, 87)( 15, 86)( 16, 85)( 17, 92)( 18, 91)( 19, 90)
( 20, 89)( 21, 96)( 22, 95)( 23, 94)( 24, 93)( 25,100)( 26, 99)( 27, 98)
( 28, 97)( 29,104)( 30,103)( 31,102)( 32,101)( 33,108)( 34,107)( 35,106)
( 36,105)( 37,112)( 38,111)( 39,110)( 40,109)( 41,116)( 42,115)( 43,114)
( 44,113)( 45,120)( 46,119)( 47,118)( 48,117)( 49,124)( 50,123)( 51,122)
( 52,121)( 53,128)( 54,127)( 55,126)( 56,125)( 57,132)( 58,131)( 59,130)
( 60,129)( 61,136)( 62,135)( 63,134)( 64,133)( 65,140)( 66,139)( 67,138)
( 68,137)( 69,144)( 70,143)( 71,142)( 72,141)( 73,148)( 74,147)( 75,146)
( 76,145);
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,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3*s2*s3 >;
to this polytope