Polytope of Type {4,6,12,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,12,2}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 5
Schlafli Type : {4,6,12,2}
Number of vertices, edges, etc : 4, 12, 36, 12, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {4,6,6,2}*576e
3-fold quotients : {4,6,4,2}*384c
4-fold quotients : {4,3,6,2}*288
6-fold quotients : {4,6,2,2}*192c
12-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144);;
s1 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)
( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)
( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)
( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)( 85, 97)
( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)( 93,101)
( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)(116,120)
(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)(128,144)
(129,137)(130,139)(131,138)(132,140);;
s2 := ( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)( 8, 98)
( 9,105)( 10,108)( 11,107)( 12,106)( 13, 89)( 14, 92)( 15, 91)( 16, 90)
( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 93)( 22, 96)( 23, 95)( 24, 94)
( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 73)( 30, 76)( 31, 75)( 32, 74)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)( 48,142)
( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)( 56,122)
( 57,129)( 58,132)( 59,131)( 60,130)( 61,113)( 62,116)( 63,115)( 64,114)
( 65,109)( 66,112)( 67,111)( 68,110)( 69,117)( 70,120)( 71,119)( 72,118);;
s3 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)( 80,120)
( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)( 88,124)
( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)( 96,128)
( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)(104,144)
(105,137)(106,138)(107,139)(108,140);;
s4 := (145,146);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144);
s1 := Sym(146)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)
( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)
( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)
( 58, 67)( 59, 66)( 60, 68)( 74, 75)( 77, 81)( 78, 83)( 79, 82)( 80, 84)
( 85, 97)( 86, 99)( 87, 98)( 88,100)( 89,105)( 90,107)( 91,106)( 92,108)
( 93,101)( 94,103)( 95,102)( 96,104)(110,111)(113,117)(114,119)(115,118)
(116,120)(121,133)(122,135)(123,134)(124,136)(125,141)(126,143)(127,142)
(128,144)(129,137)(130,139)(131,138)(132,140);
s2 := Sym(146)!( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)
( 8, 98)( 9,105)( 10,108)( 11,107)( 12,106)( 13, 89)( 14, 92)( 15, 91)
( 16, 90)( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 93)( 22, 96)( 23, 95)
( 24, 94)( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 73)( 30, 76)( 31, 75)
( 32, 74)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)
( 48,142)( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)
( 56,122)( 57,129)( 58,132)( 59,131)( 60,130)( 61,113)( 62,116)( 63,115)
( 64,114)( 65,109)( 66,112)( 67,111)( 68,110)( 69,117)( 70,120)( 71,119)
( 72,118);
s3 := Sym(146)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 73,109)( 74,110)( 75,111)( 76,112)( 77,117)( 78,118)( 79,119)
( 80,120)( 81,113)( 82,114)( 83,115)( 84,116)( 85,121)( 86,122)( 87,123)
( 88,124)( 89,129)( 90,130)( 91,131)( 92,132)( 93,125)( 94,126)( 95,127)
( 96,128)( 97,133)( 98,134)( 99,135)(100,136)(101,141)(102,142)(103,143)
(104,144)(105,137)(106,138)(107,139)(108,140);
s4 := Sym(146)!(145,146);
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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope