Polytope of Type {2,2,4,9,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,9,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,157449)
Rank : 6
Schlafli Type : {2,2,4,9,4}
Number of vertices, edges, etc : 2, 2, 4, 18, 18, 4
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
3-fold quotients : {2,2,4,3,4}*384
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)
( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)
( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)
( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)
(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)
(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)
(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148);;
s3 := ( 6, 7)( 9, 13)( 10, 15)( 11, 14)( 12, 16)( 18, 19)( 21, 37)( 22, 39)
( 23, 38)( 24, 40)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)
( 31, 42)( 32, 44)( 33, 49)( 34, 51)( 35, 50)( 36, 52)( 53,117)( 54,119)
( 55,118)( 56,120)( 57,125)( 58,127)( 59,126)( 60,128)( 61,121)( 62,123)
( 63,122)( 64,124)( 65,129)( 66,131)( 67,130)( 68,132)( 69,101)( 70,103)
( 71,102)( 72,104)( 73,109)( 74,111)( 75,110)( 76,112)( 77,105)( 78,107)
( 79,106)( 80,108)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)( 86,135)
( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)( 94,139)
( 95,138)( 96,140)( 97,145)( 98,147)( 99,146)(100,148);;
s4 := ( 5,101)( 6,102)( 7,104)( 8,103)( 9,113)( 10,114)( 11,116)( 12,115)
( 13,109)( 14,110)( 15,112)( 16,111)( 17,105)( 18,106)( 19,108)( 20,107)
( 21,133)( 22,134)( 23,136)( 24,135)( 25,145)( 26,146)( 27,148)( 28,147)
( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)
( 37,117)( 38,118)( 39,120)( 40,119)( 41,129)( 42,130)( 43,132)( 44,131)
( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)
( 55, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 63, 64)( 69, 85)( 70, 86)
( 71, 88)( 72, 87)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)( 78, 94)
( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91);;
s5 := ( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)( 12, 16)
( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 69, 81)( 70, 82)( 71, 83)( 72, 84)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,113)(102,114)(103,115)(104,116)(105,109)(106,110)(107,111)(108,112)
(117,129)(118,130)(119,131)(120,132)(121,125)(122,126)(123,127)(124,128)
(133,145)(134,146)(135,147)(136,148)(137,141)(138,142)(139,143)(140,144);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s5*s4*s3*s5*s4*s5*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, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)
( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)
( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)
( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)
( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)
( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)
( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)
(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)
(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)
(147,148);
s3 := Sym(148)!( 6, 7)( 9, 13)( 10, 15)( 11, 14)( 12, 16)( 18, 19)( 21, 37)
( 22, 39)( 23, 38)( 24, 40)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)
( 30, 43)( 31, 42)( 32, 44)( 33, 49)( 34, 51)( 35, 50)( 36, 52)( 53,117)
( 54,119)( 55,118)( 56,120)( 57,125)( 58,127)( 59,126)( 60,128)( 61,121)
( 62,123)( 63,122)( 64,124)( 65,129)( 66,131)( 67,130)( 68,132)( 69,101)
( 70,103)( 71,102)( 72,104)( 73,109)( 74,111)( 75,110)( 76,112)( 77,105)
( 78,107)( 79,106)( 80,108)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)
( 86,135)( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)
( 94,139)( 95,138)( 96,140)( 97,145)( 98,147)( 99,146)(100,148);
s4 := Sym(148)!( 5,101)( 6,102)( 7,104)( 8,103)( 9,113)( 10,114)( 11,116)
( 12,115)( 13,109)( 14,110)( 15,112)( 16,111)( 17,105)( 18,106)( 19,108)
( 20,107)( 21,133)( 22,134)( 23,136)( 24,135)( 25,145)( 26,146)( 27,148)
( 28,147)( 29,141)( 30,142)( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)
( 36,139)( 37,117)( 38,118)( 39,120)( 40,119)( 41,129)( 42,130)( 43,132)
( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)
( 52,123)( 55, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 63, 64)( 69, 85)
( 70, 86)( 71, 88)( 72, 87)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)
( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91);
s5 := Sym(148)!( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)
( 12, 16)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 69, 81)( 70, 82)( 71, 83)( 72, 84)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,113)(102,114)(103,115)(104,116)(105,109)(106,110)(107,111)
(108,112)(117,129)(118,130)(119,131)(120,132)(121,125)(122,126)(123,127)
(124,128)(133,145)(134,146)(135,147)(136,148)(137,141)(138,142)(139,143)
(140,144);
poly := sub<Sym(148)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s5*s4*s3*s5*s4*s5*s4*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope