Polytope of Type {6,3,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,8,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {6,3,8,2}
Number of vertices, edges, etc : 6, 18, 24, 16, 2
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 : {6,3,4,2}*576
3-fold quotients : {2,3,8,2}*384
4-fold quotients : {6,3,4,2}*288
6-fold quotients : {2,3,4,2}*192
8-fold quotients : {6,3,2,2}*144
12-fold quotients : {2,3,4,2}*96
24-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144);;
s1 := ( 1, 9)( 2, 10)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 16)( 8, 15)
( 19, 22)( 20, 21)( 23, 24)( 25, 57)( 26, 58)( 27, 62)( 28, 61)( 29, 60)
( 30, 59)( 31, 64)( 32, 63)( 33, 49)( 34, 50)( 35, 54)( 36, 53)( 37, 52)
( 38, 51)( 39, 56)( 40, 55)( 41, 65)( 42, 66)( 43, 70)( 44, 69)( 45, 68)
( 46, 67)( 47, 72)( 48, 71)( 73, 82)( 74, 81)( 75, 85)( 76, 86)( 77, 83)
( 78, 84)( 79, 87)( 80, 88)( 89, 90)( 91, 93)( 92, 94)( 97,130)( 98,129)
( 99,133)(100,134)(101,131)(102,132)(103,135)(104,136)(105,122)(106,121)
(107,125)(108,126)(109,123)(110,124)(111,127)(112,128)(113,138)(114,137)
(115,141)(116,142)(117,139)(118,140)(119,143)(120,144);;
s2 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)
( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)
( 62, 72)( 63, 69)( 64, 70)( 73, 98)( 74, 97)( 75, 99)( 76,100)( 77,104)
( 78,103)( 79,102)( 80,101)( 81,114)( 82,113)( 83,115)( 84,116)( 85,120)
( 86,119)( 87,118)( 88,117)( 89,106)( 90,105)( 91,107)( 92,108)( 93,112)
( 94,111)( 95,110)( 96,109)(121,122)(125,128)(126,127)(129,138)(130,137)
(131,139)(132,140)(133,144)(134,143)(135,142)(136,141);;
s3 := ( 1, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 74)( 8, 73)
( 9, 87)( 10, 88)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 82)( 16, 81)
( 17, 95)( 18, 96)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 90)( 24, 89)
( 25,103)( 26,104)( 27,101)( 28,102)( 29,100)( 30, 99)( 31, 98)( 32, 97)
( 33,111)( 34,112)( 35,109)( 36,110)( 37,108)( 38,107)( 39,106)( 40,105)
( 41,119)( 42,120)( 43,117)( 44,118)( 45,116)( 46,115)( 47,114)( 48,113)
( 49,127)( 50,128)( 51,125)( 52,126)( 53,124)( 54,123)( 55,122)( 56,121)
( 57,135)( 58,136)( 59,133)( 60,134)( 61,132)( 62,131)( 63,130)( 64,129)
( 65,143)( 66,144)( 67,141)( 68,142)( 69,140)( 70,139)( 71,138)( 72,137);;
s4 := (145,146);;
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*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,
s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144);
s1 := Sym(146)!( 1, 9)( 2, 10)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 16)
( 8, 15)( 19, 22)( 20, 21)( 23, 24)( 25, 57)( 26, 58)( 27, 62)( 28, 61)
( 29, 60)( 30, 59)( 31, 64)( 32, 63)( 33, 49)( 34, 50)( 35, 54)( 36, 53)
( 37, 52)( 38, 51)( 39, 56)( 40, 55)( 41, 65)( 42, 66)( 43, 70)( 44, 69)
( 45, 68)( 46, 67)( 47, 72)( 48, 71)( 73, 82)( 74, 81)( 75, 85)( 76, 86)
( 77, 83)( 78, 84)( 79, 87)( 80, 88)( 89, 90)( 91, 93)( 92, 94)( 97,130)
( 98,129)( 99,133)(100,134)(101,131)(102,132)(103,135)(104,136)(105,122)
(106,121)(107,125)(108,126)(109,123)(110,124)(111,127)(112,128)(113,138)
(114,137)(115,141)(116,142)(117,139)(118,140)(119,143)(120,144);
s2 := Sym(146)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)
( 8, 30)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 51, 52)( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)
( 61, 71)( 62, 72)( 63, 69)( 64, 70)( 73, 98)( 74, 97)( 75, 99)( 76,100)
( 77,104)( 78,103)( 79,102)( 80,101)( 81,114)( 82,113)( 83,115)( 84,116)
( 85,120)( 86,119)( 87,118)( 88,117)( 89,106)( 90,105)( 91,107)( 92,108)
( 93,112)( 94,111)( 95,110)( 96,109)(121,122)(125,128)(126,127)(129,138)
(130,137)(131,139)(132,140)(133,144)(134,143)(135,142)(136,141);
s3 := Sym(146)!( 1, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 74)
( 8, 73)( 9, 87)( 10, 88)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 82)
( 16, 81)( 17, 95)( 18, 96)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 90)
( 24, 89)( 25,103)( 26,104)( 27,101)( 28,102)( 29,100)( 30, 99)( 31, 98)
( 32, 97)( 33,111)( 34,112)( 35,109)( 36,110)( 37,108)( 38,107)( 39,106)
( 40,105)( 41,119)( 42,120)( 43,117)( 44,118)( 45,116)( 46,115)( 47,114)
( 48,113)( 49,127)( 50,128)( 51,125)( 52,126)( 53,124)( 54,123)( 55,122)
( 56,121)( 57,135)( 58,136)( 59,133)( 60,134)( 61,132)( 62,131)( 63,130)
( 64,129)( 65,143)( 66,144)( 67,141)( 68,142)( 69,140)( 70,139)( 71,138)
( 72,137);
s4 := Sym(146)!(145,146);
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*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, s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;
to this polytope