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