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