Polytope of Type {2,6,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,6,8,3}
Number of vertices, edges, etc : 2, 6, 48, 24, 6
Order of s0s1s2s3s4 : 12
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 : {2,6,4,3}*576
3-fold quotients : {2,2,8,3}*384
6-fold quotients : {2,2,4,3}*192
8-fold quotients : {2,6,2,3}*144
12-fold quotients : {2,2,4,3}*96
16-fold quotients : {2,3,2,3}*72
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)( 18, 26)
( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)
( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)
( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)
(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)(114,122)
(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146);;
s2 := ( 3, 87)( 4, 88)( 5, 90)( 6, 89)( 7, 84)( 8, 83)( 9, 85)( 10, 86)
( 11, 79)( 12, 80)( 13, 82)( 14, 81)( 15, 76)( 16, 75)( 17, 77)( 18, 78)
( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)( 26, 94)
( 27,111)( 28,112)( 29,114)( 30,113)( 31,108)( 32,107)( 33,109)( 34,110)
( 35,103)( 36,104)( 37,106)( 38,105)( 39,100)( 40, 99)( 41,101)( 42,102)
( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)( 50,118)
( 51,135)( 52,136)( 53,138)( 54,137)( 55,132)( 56,131)( 57,133)( 58,134)
( 59,127)( 60,128)( 61,130)( 62,129)( 63,124)( 64,123)( 65,125)( 66,126)
( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)( 74,142);;
s3 := ( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)
( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)( 33, 58)
( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 66)
( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 74)
( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)
(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)
(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)
(121,145)(122,146);;
s4 := ( 3, 51)( 4, 52)( 5, 57)( 6, 58)( 7, 56)( 8, 55)( 9, 53)( 10, 54)
( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)( 18, 62)
( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)( 26, 70)
( 29, 33)( 30, 34)( 31, 32)( 37, 41)( 38, 42)( 39, 40)( 45, 49)( 46, 50)
( 47, 48)( 75,124)( 76,123)( 77,130)( 78,129)( 79,127)( 80,128)( 81,126)
( 82,125)( 83,132)( 84,131)( 85,138)( 86,137)( 87,135)( 88,136)( 89,134)
( 90,133)( 91,140)( 92,139)( 93,146)( 94,145)( 95,143)( 96,144)( 97,142)
( 98,141)( 99,100)(101,106)(102,105)(107,108)(109,114)(110,113)(115,116)
(117,122)(118,121);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*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)!( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)( 17, 25)
( 18, 26)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)
( 42, 50)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)
( 66, 74)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)
( 90, 98)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)(113,121)
(114,122)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)
(138,146);
s2 := Sym(146)!( 3, 87)( 4, 88)( 5, 90)( 6, 89)( 7, 84)( 8, 83)( 9, 85)
( 10, 86)( 11, 79)( 12, 80)( 13, 82)( 14, 81)( 15, 76)( 16, 75)( 17, 77)
( 18, 78)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 92)( 24, 91)( 25, 93)
( 26, 94)( 27,111)( 28,112)( 29,114)( 30,113)( 31,108)( 32,107)( 33,109)
( 34,110)( 35,103)( 36,104)( 37,106)( 38,105)( 39,100)( 40, 99)( 41,101)
( 42,102)( 43,119)( 44,120)( 45,122)( 46,121)( 47,116)( 48,115)( 49,117)
( 50,118)( 51,135)( 52,136)( 53,138)( 54,137)( 55,132)( 56,131)( 57,133)
( 58,134)( 59,127)( 60,128)( 61,130)( 62,129)( 63,124)( 64,123)( 65,125)
( 66,126)( 67,143)( 68,144)( 69,146)( 70,145)( 71,140)( 72,139)( 73,141)
( 74,142);
s3 := Sym(146)!( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)
( 22, 23)( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)
( 33, 58)( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)
( 41, 66)( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)
( 49, 74)( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)
(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)
(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)
(120,142)(121,145)(122,146);
s4 := Sym(146)!( 3, 51)( 4, 52)( 5, 57)( 6, 58)( 7, 56)( 8, 55)( 9, 53)
( 10, 54)( 11, 59)( 12, 60)( 13, 65)( 14, 66)( 15, 64)( 16, 63)( 17, 61)
( 18, 62)( 19, 67)( 20, 68)( 21, 73)( 22, 74)( 23, 72)( 24, 71)( 25, 69)
( 26, 70)( 29, 33)( 30, 34)( 31, 32)( 37, 41)( 38, 42)( 39, 40)( 45, 49)
( 46, 50)( 47, 48)( 75,124)( 76,123)( 77,130)( 78,129)( 79,127)( 80,128)
( 81,126)( 82,125)( 83,132)( 84,131)( 85,138)( 86,137)( 87,135)( 88,136)
( 89,134)( 90,133)( 91,140)( 92,139)( 93,146)( 94,145)( 95,143)( 96,144)
( 97,142)( 98,141)( 99,100)(101,106)(102,105)(107,108)(109,114)(110,113)
(115,116)(117,122)(118,121);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope