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