Polytope of Type {2,8,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 5
Schlafli Type : {2,8,6,6}
Number of vertices, edges, etc : 2, 8, 24, 18, 6
Order of s0s1s2s3s4 : 24
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 : {2,8,6,3}*576, {2,4,6,6}*576c
3-fold quotients : {2,8,2,6}*384
4-fold quotients : {2,4,6,3}*288, {2,2,6,6}*288b
6-fold quotients : {2,8,2,3}*192, {2,4,2,6}*192
8-fold quotients : {2,2,6,3}*144
9-fold quotients : {2,8,2,2}*128
12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
18-fold quotients : {2,4,2,2}*64
24-fold quotients : {2,2,2,3}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 39)( 4, 40)( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 45)( 10, 46)
( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 53)( 18, 54)
( 19, 55)( 20, 56)( 21, 66)( 22, 67)( 23, 68)( 24, 69)( 25, 70)( 26, 71)
( 27, 72)( 28, 73)( 29, 74)( 30, 57)( 31, 58)( 32, 59)( 33, 60)( 34, 61)
( 35, 62)( 36, 63)( 37, 64)( 38, 65)( 75,111)( 76,112)( 77,113)( 78,114)
( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)( 86,122)
( 87,123)( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,138)( 94,139)
( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,129)
(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)(110,137);;
s2 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)
( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 39, 57)
( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)( 47, 64)
( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)( 55, 74)
( 56, 73)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 93,102)
( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)(100,110)(101,109)
(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)
(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)
(127,146)(128,145);;
s3 := ( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 13)( 15, 19)( 16, 18)( 17, 20)
( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 31)( 33, 37)( 34, 36)( 35, 38)
( 39, 40)( 42, 46)( 43, 45)( 44, 47)( 48, 49)( 51, 55)( 52, 54)( 53, 56)
( 57, 58)( 60, 64)( 61, 63)( 62, 65)( 66, 67)( 69, 73)( 70, 72)( 71, 74)
( 75, 76)( 78, 82)( 79, 81)( 80, 83)( 84, 85)( 87, 91)( 88, 90)( 89, 92)
( 93, 94)( 96,100)( 97, 99)( 98,101)(102,103)(105,109)(106,108)(107,110)
(111,112)(114,118)(115,117)(116,119)(120,121)(123,127)(124,126)(125,128)
(129,130)(132,136)(133,135)(134,137)(138,139)(141,145)(142,144)(143,146);;
s4 := ( 3, 78)( 4, 80)( 5, 79)( 6, 75)( 7, 77)( 8, 76)( 9, 81)( 10, 83)
( 11, 82)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)( 18, 90)
( 19, 92)( 20, 91)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)( 26, 94)
( 27, 99)( 28,101)( 29,100)( 30,105)( 31,107)( 32,106)( 33,102)( 34,104)
( 35,103)( 36,108)( 37,110)( 38,109)( 39,114)( 40,116)( 41,115)( 42,111)
( 43,113)( 44,112)( 45,117)( 46,119)( 47,118)( 48,123)( 49,125)( 50,124)
( 51,120)( 52,122)( 53,121)( 54,126)( 55,128)( 56,127)( 57,132)( 58,134)
( 59,133)( 60,129)( 61,131)( 62,130)( 63,135)( 64,137)( 65,136)( 66,141)
( 67,143)( 68,142)( 69,138)( 70,140)( 71,139)( 72,144)( 73,146)( 74,145);;
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*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 3, 39)( 4, 40)( 5, 41)( 6, 42)( 7, 43)( 8, 44)( 9, 45)
( 10, 46)( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 53)
( 18, 54)( 19, 55)( 20, 56)( 21, 66)( 22, 67)( 23, 68)( 24, 69)( 25, 70)
( 26, 71)( 27, 72)( 28, 73)( 29, 74)( 30, 57)( 31, 58)( 32, 59)( 33, 60)
( 34, 61)( 35, 62)( 36, 63)( 37, 64)( 38, 65)( 75,111)( 76,112)( 77,113)
( 78,114)( 79,115)( 80,116)( 81,117)( 82,118)( 83,119)( 84,120)( 85,121)
( 86,122)( 87,123)( 88,124)( 89,125)( 90,126)( 91,127)( 92,128)( 93,138)
( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)
(102,129)(103,130)(104,131)(105,132)(106,133)(107,134)(108,135)(109,136)
(110,137);
s2 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)
( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)
( 39, 57)( 40, 59)( 41, 58)( 42, 60)( 43, 62)( 44, 61)( 45, 63)( 46, 65)
( 47, 64)( 48, 66)( 49, 68)( 50, 67)( 51, 69)( 52, 71)( 53, 70)( 54, 72)
( 55, 74)( 56, 73)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)
( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)(100,110)
(101,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)
(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)
(126,144)(127,146)(128,145);
s3 := Sym(146)!( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 13)( 15, 19)( 16, 18)
( 17, 20)( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 31)( 33, 37)( 34, 36)
( 35, 38)( 39, 40)( 42, 46)( 43, 45)( 44, 47)( 48, 49)( 51, 55)( 52, 54)
( 53, 56)( 57, 58)( 60, 64)( 61, 63)( 62, 65)( 66, 67)( 69, 73)( 70, 72)
( 71, 74)( 75, 76)( 78, 82)( 79, 81)( 80, 83)( 84, 85)( 87, 91)( 88, 90)
( 89, 92)( 93, 94)( 96,100)( 97, 99)( 98,101)(102,103)(105,109)(106,108)
(107,110)(111,112)(114,118)(115,117)(116,119)(120,121)(123,127)(124,126)
(125,128)(129,130)(132,136)(133,135)(134,137)(138,139)(141,145)(142,144)
(143,146);
s4 := Sym(146)!( 3, 78)( 4, 80)( 5, 79)( 6, 75)( 7, 77)( 8, 76)( 9, 81)
( 10, 83)( 11, 82)( 12, 87)( 13, 89)( 14, 88)( 15, 84)( 16, 86)( 17, 85)
( 18, 90)( 19, 92)( 20, 91)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)
( 26, 94)( 27, 99)( 28,101)( 29,100)( 30,105)( 31,107)( 32,106)( 33,102)
( 34,104)( 35,103)( 36,108)( 37,110)( 38,109)( 39,114)( 40,116)( 41,115)
( 42,111)( 43,113)( 44,112)( 45,117)( 46,119)( 47,118)( 48,123)( 49,125)
( 50,124)( 51,120)( 52,122)( 53,121)( 54,126)( 55,128)( 56,127)( 57,132)
( 58,134)( 59,133)( 60,129)( 61,131)( 62,130)( 63,135)( 64,137)( 65,136)
( 66,141)( 67,143)( 68,142)( 69,138)( 70,140)( 71,139)( 72,144)( 73,146)
( 74,145);
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*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope