Polytope of Type {2,4,4,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,9}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 5
Schlafli Type : {2,4,4,9}
Number of vertices, edges, etc : 2, 8, 16, 36, 9
Order of s0s1s2s3s4 : 18
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) :
3-fold quotients : {2,4,4,3}*384a
4-fold quotients : {2,2,4,9}*288
12-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 9)( 8, 10)( 11, 14)( 12, 13)( 15, 16)( 17, 18)( 23, 25)( 24, 26)
( 27, 30)( 28, 29)( 31, 32)( 33, 34)( 39, 41)( 40, 42)( 43, 46)( 44, 45)
( 47, 48)( 49, 50)( 55, 57)( 56, 58)( 59, 62)( 60, 61)( 63, 64)( 65, 66)
( 71, 73)( 72, 74)( 75, 78)( 76, 77)( 79, 80)( 81, 82)( 87, 89)( 88, 90)
( 91, 94)( 92, 93)( 95, 96)( 97, 98)(103,105)(104,106)(107,110)(108,109)
(111,112)(113,114)(119,121)(120,122)(123,126)(124,125)(127,128)(129,130)
(135,137)(136,138)(139,142)(140,141)(143,144)(145,146);;
s2 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146);;
s3 := ( 5, 6)( 7, 11)( 8, 12)( 9, 14)( 10, 13)( 17, 18)( 19, 35)( 20, 36)
( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)( 28, 40)
( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)( 52,116)
( 53,118)( 54,117)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)( 60,120)
( 61,122)( 62,121)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)( 68,100)
( 69,102)( 70,101)( 71,107)( 72,108)( 73,110)( 74,109)( 75,103)( 76,104)
( 77,106)( 78,105)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)( 84,132)
( 85,134)( 86,133)( 87,139)( 88,140)( 89,142)( 90,141)( 91,135)( 92,136)
( 93,138)( 94,137)( 95,143)( 96,144)( 97,146)( 98,145);;
s4 := ( 3, 99)( 4,101)( 5,100)( 6,102)( 7,111)( 8,113)( 9,112)( 10,114)
( 11,107)( 12,109)( 13,108)( 14,110)( 15,103)( 16,105)( 17,104)( 18,106)
( 19,131)( 20,133)( 21,132)( 22,134)( 23,143)( 24,145)( 25,144)( 26,146)
( 27,139)( 28,141)( 29,140)( 30,142)( 31,135)( 32,137)( 33,136)( 34,138)
( 35,115)( 36,117)( 37,116)( 38,118)( 39,127)( 40,129)( 41,128)( 42,130)
( 43,123)( 44,125)( 45,124)( 46,126)( 47,119)( 48,121)( 49,120)( 50,122)
( 52, 53)( 55, 63)( 56, 65)( 57, 64)( 58, 66)( 60, 61)( 67, 83)( 68, 85)
( 69, 84)( 70, 86)( 71, 95)( 72, 97)( 73, 96)( 74, 98)( 75, 91)( 76, 93)
( 77, 92)( 78, 94)( 79, 87)( 80, 89)( 81, 88)( 82, 90);;
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*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
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(146)!(1,2);
s1 := Sym(146)!( 7, 9)( 8, 10)( 11, 14)( 12, 13)( 15, 16)( 17, 18)( 23, 25)
( 24, 26)( 27, 30)( 28, 29)( 31, 32)( 33, 34)( 39, 41)( 40, 42)( 43, 46)
( 44, 45)( 47, 48)( 49, 50)( 55, 57)( 56, 58)( 59, 62)( 60, 61)( 63, 64)
( 65, 66)( 71, 73)( 72, 74)( 75, 78)( 76, 77)( 79, 80)( 81, 82)( 87, 89)
( 88, 90)( 91, 94)( 92, 93)( 95, 96)( 97, 98)(103,105)(104,106)(107,110)
(108,109)(111,112)(113,114)(119,121)(120,122)(123,126)(124,125)(127,128)
(129,130)(135,137)(136,138)(139,142)(140,141)(143,144)(145,146);
s2 := Sym(146)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)
( 74, 82)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(121,129)
(122,130)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146);
s3 := Sym(146)!( 5, 6)( 7, 11)( 8, 12)( 9, 14)( 10, 13)( 17, 18)( 19, 35)
( 20, 36)( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)
( 28, 40)( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)
( 52,116)( 53,118)( 54,117)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)
( 60,120)( 61,122)( 62,121)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)
( 68,100)( 69,102)( 70,101)( 71,107)( 72,108)( 73,110)( 74,109)( 75,103)
( 76,104)( 77,106)( 78,105)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)
( 84,132)( 85,134)( 86,133)( 87,139)( 88,140)( 89,142)( 90,141)( 91,135)
( 92,136)( 93,138)( 94,137)( 95,143)( 96,144)( 97,146)( 98,145);
s4 := Sym(146)!( 3, 99)( 4,101)( 5,100)( 6,102)( 7,111)( 8,113)( 9,112)
( 10,114)( 11,107)( 12,109)( 13,108)( 14,110)( 15,103)( 16,105)( 17,104)
( 18,106)( 19,131)( 20,133)( 21,132)( 22,134)( 23,143)( 24,145)( 25,144)
( 26,146)( 27,139)( 28,141)( 29,140)( 30,142)( 31,135)( 32,137)( 33,136)
( 34,138)( 35,115)( 36,117)( 37,116)( 38,118)( 39,127)( 40,129)( 41,128)
( 42,130)( 43,123)( 44,125)( 45,124)( 46,126)( 47,119)( 48,121)( 49,120)
( 50,122)( 52, 53)( 55, 63)( 56, 65)( 57, 64)( 58, 66)( 60, 61)( 67, 83)
( 68, 85)( 69, 84)( 70, 86)( 71, 95)( 72, 97)( 73, 96)( 74, 98)( 75, 91)
( 76, 93)( 77, 92)( 78, 94)( 79, 87)( 80, 89)( 81, 88)( 82, 90);
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope