Polytope of Type {2,4,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,4,6,6}
Number of vertices, edges, etc : 2, 8, 24, 36, 6
Order of s0s1s2s3s4 : 6
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 : {2,4,3,6}*576, {2,4,6,6}*576e, {2,4,6,6}*576f
3-fold quotients : {2,4,6,2}*384
4-fold quotients : {2,4,3,6}*288, {2,2,6,6}*288c
6-fold quotients : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
8-fold quotients : {2,2,3,6}*144
12-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
24-fold quotients : {2,2,3,2}*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 := ( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 81)( 8, 82)( 9, 79)( 10, 80)
( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)( 18, 88)
( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)( 26, 96)
( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)( 34,104)
( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)( 42,112)
( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)( 50,120)
( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)( 58,128)
( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)( 66,136)
( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)( 74,144);;
s2 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)
( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)
( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)
( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)
( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)
( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)
(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)
(131,139)(132,141)(133,140)(134,142);;
s3 := ( 3, 67)( 4, 70)( 5, 69)( 6, 68)( 7, 63)( 8, 66)( 9, 65)( 10, 64)
( 11, 71)( 12, 74)( 13, 73)( 14, 72)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 59)( 24, 62)( 25, 61)( 26, 60)
( 27, 43)( 28, 46)( 29, 45)( 30, 44)( 31, 39)( 32, 42)( 33, 41)( 34, 40)
( 35, 47)( 36, 50)( 37, 49)( 38, 48)( 75,139)( 76,142)( 77,141)( 78,140)
( 79,135)( 80,138)( 81,137)( 82,136)( 83,143)( 84,146)( 85,145)( 86,144)
( 87,127)( 88,130)( 89,129)( 90,128)( 91,123)( 92,126)( 93,125)( 94,124)
( 95,131)( 96,134)( 97,133)( 98,132)( 99,115)(100,118)(101,117)(102,116)
(103,111)(104,114)(105,113)(106,112)(107,119)(108,122)(109,121)(110,120);;
s4 := ( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)( 22, 26)
( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)( 70, 74)
( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(103,107)(104,108)(105,109)(106,110)(115,119)(116,120)(117,121)(118,122)
(127,131)(128,132)(129,133)(130,134)(139,143)(140,144)(141,145)(142,146);;
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*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*s1*s2*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 3, 77)( 4, 78)( 5, 75)( 6, 76)( 7, 81)( 8, 82)( 9, 79)
( 10, 80)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 89)( 16, 90)( 17, 87)
( 18, 88)( 19, 93)( 20, 94)( 21, 91)( 22, 92)( 23, 97)( 24, 98)( 25, 95)
( 26, 96)( 27,101)( 28,102)( 29, 99)( 30,100)( 31,105)( 32,106)( 33,103)
( 34,104)( 35,109)( 36,110)( 37,107)( 38,108)( 39,113)( 40,114)( 41,111)
( 42,112)( 43,117)( 44,118)( 45,115)( 46,116)( 47,121)( 48,122)( 49,119)
( 50,120)( 51,125)( 52,126)( 53,123)( 54,124)( 55,129)( 56,130)( 57,127)
( 58,128)( 59,133)( 60,134)( 61,131)( 62,132)( 63,137)( 64,138)( 65,135)
( 66,136)( 67,141)( 68,142)( 69,139)( 70,140)( 71,145)( 72,146)( 73,143)
( 74,144);
s2 := Sym(146)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)
( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)
( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)
( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)
( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)
( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)
(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)
(130,146)(131,139)(132,141)(133,140)(134,142);
s3 := Sym(146)!( 3, 67)( 4, 70)( 5, 69)( 6, 68)( 7, 63)( 8, 66)( 9, 65)
( 10, 64)( 11, 71)( 12, 74)( 13, 73)( 14, 72)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 59)( 24, 62)( 25, 61)
( 26, 60)( 27, 43)( 28, 46)( 29, 45)( 30, 44)( 31, 39)( 32, 42)( 33, 41)
( 34, 40)( 35, 47)( 36, 50)( 37, 49)( 38, 48)( 75,139)( 76,142)( 77,141)
( 78,140)( 79,135)( 80,138)( 81,137)( 82,136)( 83,143)( 84,146)( 85,145)
( 86,144)( 87,127)( 88,130)( 89,129)( 90,128)( 91,123)( 92,126)( 93,125)
( 94,124)( 95,131)( 96,134)( 97,133)( 98,132)( 99,115)(100,118)(101,117)
(102,116)(103,111)(104,114)(105,113)(106,112)(107,119)(108,122)(109,121)
(110,120);
s4 := Sym(146)!( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)
( 22, 26)( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)
( 70, 74)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(103,107)(104,108)(105,109)(106,110)(115,119)(116,120)(117,121)
(118,122)(127,131)(128,132)(129,133)(130,134)(139,143)(140,144)(141,145)
(142,146);
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*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*s1*s2*s1*s2*s1*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >;
to this polytope