Polytope of Type {2,6,3,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,6,3,8}
Number of vertices, edges, etc : 2, 6, 18, 24, 16
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 : {2,6,3,4}*576
3-fold quotients : {2,2,3,8}*384
4-fold quotients : {2,6,3,4}*288
6-fold quotients : {2,2,3,4}*192
8-fold quotients : {2,6,3,2}*144
12-fold quotients : {2,2,3,4}*96
24-fold quotients : {2,2,3,2}*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, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)( 10, 17)
( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)( 31, 62)
( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)( 39, 54)
( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)
( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)( 79, 85)
( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)(100,131)
(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)(108,123)
(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)(116,139)
(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);;
s3 := ( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)( 10, 32)
( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)
( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)( 26, 40)
( 53, 54)( 55, 57)( 56, 58)( 59, 67)( 60, 68)( 61, 70)( 62, 69)( 63, 73)
( 64, 74)( 65, 71)( 66, 72)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)
( 80,105)( 81,104)( 82,103)( 83,116)( 84,115)( 85,117)( 86,118)( 87,122)
( 88,121)( 89,120)( 90,119)( 91,108)( 92,107)( 93,109)( 94,110)( 95,114)
( 96,113)( 97,112)( 98,111)(123,124)(127,130)(128,129)(131,140)(132,139)
(133,141)(134,142)(135,146)(136,145)(137,144)(138,143);;
s4 := ( 3, 81)( 4, 82)( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 76)( 10, 75)
( 11, 89)( 12, 90)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 84)( 18, 83)
( 19, 97)( 20, 98)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 92)( 26, 91)
( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)( 34, 99)
( 35,113)( 36,114)( 37,111)( 38,112)( 39,110)( 40,109)( 41,108)( 42,107)
( 43,121)( 44,122)( 45,119)( 46,120)( 47,118)( 48,117)( 49,116)( 50,115)
( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)( 58,123)
( 59,137)( 60,138)( 61,135)( 62,136)( 63,134)( 64,133)( 65,132)( 66,131)
( 67,145)( 68,146)( 69,143)( 70,144)( 71,142)( 72,141)( 73,140)( 74,139);;
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,
s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*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, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)
( 10, 17)( 21, 24)( 22, 23)( 25, 26)( 27, 59)( 28, 60)( 29, 64)( 30, 63)
( 31, 62)( 32, 61)( 33, 66)( 34, 65)( 35, 51)( 36, 52)( 37, 56)( 38, 55)
( 39, 54)( 40, 53)( 41, 58)( 42, 57)( 43, 67)( 44, 68)( 45, 72)( 46, 71)
( 47, 70)( 48, 69)( 49, 74)( 50, 73)( 75, 84)( 76, 83)( 77, 87)( 78, 88)
( 79, 85)( 80, 86)( 81, 89)( 82, 90)( 91, 92)( 93, 95)( 94, 96)( 99,132)
(100,131)(101,135)(102,136)(103,133)(104,134)(105,137)(106,138)(107,124)
(108,123)(109,127)(110,128)(111,125)(112,126)(113,129)(114,130)(115,140)
(116,139)(117,143)(118,144)(119,141)(120,142)(121,145)(122,146);
s3 := Sym(146)!( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)
( 10, 32)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)
( 18, 48)( 19, 35)( 20, 36)( 21, 38)( 22, 37)( 23, 41)( 24, 42)( 25, 39)
( 26, 40)( 53, 54)( 55, 57)( 56, 58)( 59, 67)( 60, 68)( 61, 70)( 62, 69)
( 63, 73)( 64, 74)( 65, 71)( 66, 72)( 75,100)( 76, 99)( 77,101)( 78,102)
( 79,106)( 80,105)( 81,104)( 82,103)( 83,116)( 84,115)( 85,117)( 86,118)
( 87,122)( 88,121)( 89,120)( 90,119)( 91,108)( 92,107)( 93,109)( 94,110)
( 95,114)( 96,113)( 97,112)( 98,111)(123,124)(127,130)(128,129)(131,140)
(132,139)(133,141)(134,142)(135,146)(136,145)(137,144)(138,143);
s4 := Sym(146)!( 3, 81)( 4, 82)( 5, 79)( 6, 80)( 7, 78)( 8, 77)( 9, 76)
( 10, 75)( 11, 89)( 12, 90)( 13, 87)( 14, 88)( 15, 86)( 16, 85)( 17, 84)
( 18, 83)( 19, 97)( 20, 98)( 21, 95)( 22, 96)( 23, 94)( 24, 93)( 25, 92)
( 26, 91)( 27,105)( 28,106)( 29,103)( 30,104)( 31,102)( 32,101)( 33,100)
( 34, 99)( 35,113)( 36,114)( 37,111)( 38,112)( 39,110)( 40,109)( 41,108)
( 42,107)( 43,121)( 44,122)( 45,119)( 46,120)( 47,118)( 48,117)( 49,116)
( 50,115)( 51,129)( 52,130)( 53,127)( 54,128)( 55,126)( 56,125)( 57,124)
( 58,123)( 59,137)( 60,138)( 61,135)( 62,136)( 63,134)( 64,133)( 65,132)
( 66,131)( 67,145)( 68,146)( 69,143)( 70,144)( 71,142)( 72,141)( 73,140)
( 74,139);
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, s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >;
to this polytope