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}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155402)
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
Non-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}*576b
3-fold quotients : {2,4,6,4}*384b
4-fold quotients : {2,2,9,4}*288
6-fold quotients : {2,2,6,4}*192c
12-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)
( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)
( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)( 98,134)
( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)(106,142)
(107,143)(108,144)(109,145)(110,146);;
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, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 23)( 8, 24)( 9, 26)( 10, 25)
( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 27, 35)( 28, 36)( 29, 38)( 30, 37)
( 33, 34)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)( 45, 62)
( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 63, 71)( 64, 72)( 65, 74)
( 66, 73)( 69, 70)( 75, 87)( 76, 88)( 77, 90)( 78, 89)( 79, 95)( 80, 96)
( 81, 98)( 82, 97)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 99,107)(100,108)
(101,110)(102,109)(105,106)(111,123)(112,124)(113,126)(114,125)(115,131)
(116,132)(117,134)(118,133)(119,127)(120,128)(121,130)(122,129)(135,143)
(136,144)(137,146)(138,145)(141,142);;
s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145);;
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, 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,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*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(146)!(1,2);
s1 := Sym(146)!( 75,111)( 76,112)( 77,113)( 78,114)( 79,115)( 80,116)( 81,117)
( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)( 87,123)( 88,124)( 89,125)
( 90,126)( 91,127)( 92,128)( 93,129)( 94,130)( 95,131)( 96,132)( 97,133)
( 98,134)( 99,135)(100,136)(101,137)(102,138)(103,139)(104,140)(105,141)
(106,142)(107,143)(108,144)(109,145)(110,146);
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, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 23)( 8, 24)( 9, 26)
( 10, 25)( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 27, 35)( 28, 36)( 29, 38)
( 30, 37)( 33, 34)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)
( 45, 62)( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 63, 71)( 64, 72)
( 65, 74)( 66, 73)( 69, 70)( 75, 87)( 76, 88)( 77, 90)( 78, 89)( 79, 95)
( 80, 96)( 81, 98)( 82, 97)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 99,107)
(100,108)(101,110)(102,109)(105,106)(111,123)(112,124)(113,126)(114,125)
(115,131)(116,132)(117,134)(118,133)(119,127)(120,128)(121,130)(122,129)
(135,143)(136,144)(137,146)(138,145)(141,142);
s4 := Sym(146)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145);
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, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*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