Polytope of Type {2,6,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 5
Schlafli Type : {2,6,6,8}
Number of vertices, edges, etc : 2, 6, 18, 24, 8
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 : {2,3,6,8}*576, {2,6,6,4}*576c
3-fold quotients : {2,6,2,8}*384
4-fold quotients : {2,3,6,4}*288, {2,6,6,2}*288c
6-fold quotients : {2,3,2,8}*192, {2,6,2,4}*192
8-fold quotients : {2,3,6,2}*144
9-fold quotients : {2,2,2,8}*128
12-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
18-fold quotients : {2,2,2,4}*64
24-fold quotients : {2,3,2,2}*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 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)
( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)
( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)
( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)( 89, 91)
( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)(107,109)
(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)(125,127)
(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)(143,145);;
s2 := ( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)
( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)
( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)( 26, 95)
( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)( 34,102)
( 35,104)( 36,109)( 37,108)( 38,110)( 39,115)( 40,114)( 41,116)( 42,112)
( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)( 50,125)
( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 57,133)( 58,132)
( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)( 66,142)
( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)( 74,146);;
s3 := ( 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);;
s4 := ( 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);;
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*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
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)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)
( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)
( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)
( 53, 55)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)
( 71, 73)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)( 88, 92)
( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)(106,110)
(107,109)(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)
(125,127)(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)
(143,145);
s2 := Sym(146)!( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)
( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)
( 18, 91)( 19, 90)( 20, 92)( 21, 97)( 22, 96)( 23, 98)( 24, 94)( 25, 93)
( 26, 95)( 27,100)( 28, 99)( 29,101)( 30,106)( 31,105)( 32,107)( 33,103)
( 34,102)( 35,104)( 36,109)( 37,108)( 38,110)( 39,115)( 40,114)( 41,116)
( 42,112)( 43,111)( 44,113)( 45,118)( 46,117)( 47,119)( 48,124)( 49,123)
( 50,125)( 51,121)( 52,120)( 53,122)( 54,127)( 55,126)( 56,128)( 57,133)
( 58,132)( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)
( 66,142)( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)
( 74,146);
s3 := 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);
s4 := 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);
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*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope