Polytope of Type {2,4,18,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,18,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,136321)
Rank : 5
Schlafli Type : {2,4,18,4}
Number of vertices, edges, etc : 2, 4, 36, 36, 4
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 : {2,2,18,4}*576a, {2,4,18,2}*576a
3-fold quotients : {2,4,6,4}*384a
4-fold quotients : {2,2,18,2}*288
6-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
8-fold quotients : {2,2,9,2}*144
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,2,6,2}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
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 := ( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)
( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)( 90,108)
( 91,109)( 92,110)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)
(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)(124,142)
(125,143)(126,144)(127,145)(128,146);;
s2 := ( 3, 75)( 4, 77)( 5, 76)( 6, 83)( 7, 82)( 8, 81)( 9, 80)( 10, 79)
( 11, 78)( 12, 84)( 13, 86)( 14, 85)( 15, 92)( 16, 91)( 17, 90)( 18, 89)
( 19, 88)( 20, 87)( 21, 93)( 22, 95)( 23, 94)( 24,101)( 25,100)( 26, 99)
( 27, 98)( 28, 97)( 29, 96)( 30,102)( 31,104)( 32,103)( 33,110)( 34,109)
( 35,108)( 36,107)( 37,106)( 38,105)( 39,129)( 40,131)( 41,130)( 42,137)
( 43,136)( 44,135)( 45,134)( 46,133)( 47,132)( 48,138)( 49,140)( 50,139)
( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)( 57,111)( 58,113)
( 59,112)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)( 66,120)
( 67,122)( 68,121)( 69,128)( 70,127)( 71,126)( 72,125)( 73,124)( 74,123);;
s3 := ( 3, 6)( 4, 8)( 5, 7)( 9, 11)( 12, 15)( 13, 17)( 14, 16)( 18, 20)
( 21, 24)( 22, 26)( 23, 25)( 27, 29)( 30, 33)( 31, 35)( 32, 34)( 36, 38)
( 39, 69)( 40, 71)( 41, 70)( 42, 66)( 43, 68)( 44, 67)( 45, 74)( 46, 73)
( 47, 72)( 48, 60)( 49, 62)( 50, 61)( 51, 57)( 52, 59)( 53, 58)( 54, 65)
( 55, 64)( 56, 63)( 75, 78)( 76, 80)( 77, 79)( 81, 83)( 84, 87)( 85, 89)
( 86, 88)( 90, 92)( 93, 96)( 94, 98)( 95, 97)( 99,101)(102,105)(103,107)
(104,106)(108,110)(111,141)(112,143)(113,142)(114,138)(115,140)(116,139)
(117,146)(118,145)(119,144)(120,132)(121,134)(122,133)(123,129)(124,131)
(125,130)(126,137)(127,136)(128,135);;
s4 := ( 3, 39)( 4, 40)( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 45)( 10, 46)
( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 53)( 18, 54)
( 19, 55)( 20, 56)( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 61)( 26, 62)
( 27, 63)( 28, 64)( 29, 65)( 30, 66)( 31, 67)( 32, 68)( 33, 69)( 34, 70)
( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,129)( 76,130)( 77,131)( 78,132)
( 79,133)( 80,134)( 81,135)( 82,136)( 83,137)( 84,138)( 85,139)( 86,140)
( 87,141)( 88,142)( 89,143)( 90,144)( 91,145)( 92,146)( 93,111)( 94,112)
( 95,113)( 96,114)( 97,115)( 98,116)( 99,117)(100,118)(101,119)(102,120)
(103,121)(104,122)(105,123)(106,124)(107,125)(108,126)(109,127)(110,128);;
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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)!( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)
( 82,100)( 83,101)( 84,102)( 85,103)( 86,104)( 87,105)( 88,106)( 89,107)
( 90,108)( 91,109)( 92,110)(111,129)(112,130)(113,131)(114,132)(115,133)
(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)
(124,142)(125,143)(126,144)(127,145)(128,146);
s2 := Sym(146)!( 3, 75)( 4, 77)( 5, 76)( 6, 83)( 7, 82)( 8, 81)( 9, 80)
( 10, 79)( 11, 78)( 12, 84)( 13, 86)( 14, 85)( 15, 92)( 16, 91)( 17, 90)
( 18, 89)( 19, 88)( 20, 87)( 21, 93)( 22, 95)( 23, 94)( 24,101)( 25,100)
( 26, 99)( 27, 98)( 28, 97)( 29, 96)( 30,102)( 31,104)( 32,103)( 33,110)
( 34,109)( 35,108)( 36,107)( 37,106)( 38,105)( 39,129)( 40,131)( 41,130)
( 42,137)( 43,136)( 44,135)( 45,134)( 46,133)( 47,132)( 48,138)( 49,140)
( 50,139)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)( 57,111)
( 58,113)( 59,112)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)
( 66,120)( 67,122)( 68,121)( 69,128)( 70,127)( 71,126)( 72,125)( 73,124)
( 74,123);
s3 := Sym(146)!( 3, 6)( 4, 8)( 5, 7)( 9, 11)( 12, 15)( 13, 17)( 14, 16)
( 18, 20)( 21, 24)( 22, 26)( 23, 25)( 27, 29)( 30, 33)( 31, 35)( 32, 34)
( 36, 38)( 39, 69)( 40, 71)( 41, 70)( 42, 66)( 43, 68)( 44, 67)( 45, 74)
( 46, 73)( 47, 72)( 48, 60)( 49, 62)( 50, 61)( 51, 57)( 52, 59)( 53, 58)
( 54, 65)( 55, 64)( 56, 63)( 75, 78)( 76, 80)( 77, 79)( 81, 83)( 84, 87)
( 85, 89)( 86, 88)( 90, 92)( 93, 96)( 94, 98)( 95, 97)( 99,101)(102,105)
(103,107)(104,106)(108,110)(111,141)(112,143)(113,142)(114,138)(115,140)
(116,139)(117,146)(118,145)(119,144)(120,132)(121,134)(122,133)(123,129)
(124,131)(125,130)(126,137)(127,136)(128,135);
s4 := Sym(146)!( 3, 39)( 4, 40)( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 45)
( 10, 46)( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 53)
( 18, 54)( 19, 55)( 20, 56)( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 61)
( 26, 62)( 27, 63)( 28, 64)( 29, 65)( 30, 66)( 31, 67)( 32, 68)( 33, 69)
( 34, 70)( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,129)( 76,130)( 77,131)
( 78,132)( 79,133)( 80,134)( 81,135)( 82,136)( 83,137)( 84,138)( 85,139)
( 86,140)( 87,141)( 88,142)( 89,143)( 90,144)( 91,145)( 92,146)( 93,111)
( 94,112)( 95,113)( 96,114)( 97,115)( 98,116)( 99,117)(100,118)(101,119)
(102,120)(103,121)(104,122)(105,123)(106,124)(107,125)(108,126)(109,127)
(110,128);
poly := sub<Sym(146)|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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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