Polytope of Type {2,4,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,136345)
Rank : 5
Schlafli Type : {2,4,6,12}
Number of vertices, edges, etc : 2, 4, 12, 36, 12
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 : {2,4,6,6}*576b, {2,2,6,12}*576c
3-fold quotients : {2,4,6,4}*384a
4-fold quotients : {2,2,6,6}*288c
6-fold quotients : {2,2,6,4}*192a, {2,4,6,2}*192a
8-fold quotients : {2,2,3,6}*144
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,2,6,2}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
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, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,120)( 40,121)( 41,122)( 42,123)
( 43,124)( 44,125)( 45,126)( 46,127)( 47,128)( 48,111)( 49,112)( 50,113)
( 51,114)( 52,115)( 53,116)( 54,117)( 55,118)( 56,119)( 57,138)( 58,139)
( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)( 64,145)( 65,146)( 66,129)
( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)( 73,136)( 74,137);;
s2 := ( 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)
( 75, 84)( 76, 86)( 77, 85)( 78, 90)( 79, 92)( 80, 91)( 81, 87)( 82, 89)
( 83, 88)( 93,102)( 94,104)( 95,103)( 96,108)( 97,110)( 98,109)( 99,105)
(100,107)(101,106)(111,120)(112,122)(113,121)(114,126)(115,128)(116,127)
(117,123)(118,125)(119,124)(129,138)(130,140)(131,139)(132,144)(133,146)
(134,145)(135,141)(136,143)(137,142);;
s3 := ( 3, 43)( 4, 42)( 5, 44)( 6, 40)( 7, 39)( 8, 41)( 9, 46)( 10, 45)
( 11, 47)( 12, 52)( 13, 51)( 14, 53)( 15, 49)( 16, 48)( 17, 50)( 18, 55)
( 19, 54)( 20, 56)( 21, 61)( 22, 60)( 23, 62)( 24, 58)( 25, 57)( 26, 59)
( 27, 64)( 28, 63)( 29, 65)( 30, 70)( 31, 69)( 32, 71)( 33, 67)( 34, 66)
( 35, 68)( 36, 73)( 37, 72)( 38, 74)( 75,124)( 76,123)( 77,125)( 78,121)
( 79,120)( 80,122)( 81,127)( 82,126)( 83,128)( 84,115)( 85,114)( 86,116)
( 87,112)( 88,111)( 89,113)( 90,118)( 91,117)( 92,119)( 93,142)( 94,141)
( 95,143)( 96,139)( 97,138)( 98,140)( 99,145)(100,144)(101,146)(102,133)
(103,132)(104,134)(105,130)(106,129)(107,131)(108,136)(109,135)(110,137);;
s4 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 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)( 94, 95)( 97, 98)(100,101)(103,104)
(106,107)(109,110)(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);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)
( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,120)( 40,121)( 41,122)
( 42,123)( 43,124)( 44,125)( 45,126)( 46,127)( 47,128)( 48,111)( 49,112)
( 50,113)( 51,114)( 52,115)( 53,116)( 54,117)( 55,118)( 56,119)( 57,138)
( 58,139)( 59,140)( 60,141)( 61,142)( 62,143)( 63,144)( 64,145)( 65,146)
( 66,129)( 67,130)( 68,131)( 69,132)( 70,133)( 71,134)( 72,135)( 73,136)
( 74,137);
s2 := 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)( 75, 84)( 76, 86)( 77, 85)( 78, 90)( 79, 92)( 80, 91)( 81, 87)
( 82, 89)( 83, 88)( 93,102)( 94,104)( 95,103)( 96,108)( 97,110)( 98,109)
( 99,105)(100,107)(101,106)(111,120)(112,122)(113,121)(114,126)(115,128)
(116,127)(117,123)(118,125)(119,124)(129,138)(130,140)(131,139)(132,144)
(133,146)(134,145)(135,141)(136,143)(137,142);
s3 := Sym(146)!( 3, 43)( 4, 42)( 5, 44)( 6, 40)( 7, 39)( 8, 41)( 9, 46)
( 10, 45)( 11, 47)( 12, 52)( 13, 51)( 14, 53)( 15, 49)( 16, 48)( 17, 50)
( 18, 55)( 19, 54)( 20, 56)( 21, 61)( 22, 60)( 23, 62)( 24, 58)( 25, 57)
( 26, 59)( 27, 64)( 28, 63)( 29, 65)( 30, 70)( 31, 69)( 32, 71)( 33, 67)
( 34, 66)( 35, 68)( 36, 73)( 37, 72)( 38, 74)( 75,124)( 76,123)( 77,125)
( 78,121)( 79,120)( 80,122)( 81,127)( 82,126)( 83,128)( 84,115)( 85,114)
( 86,116)( 87,112)( 88,111)( 89,113)( 90,118)( 91,117)( 92,119)( 93,142)
( 94,141)( 95,143)( 96,139)( 97,138)( 98,140)( 99,145)(100,144)(101,146)
(102,133)(103,132)(104,134)(105,130)(106,129)(107,131)(108,136)(109,135)
(110,137);
s4 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 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)( 94, 95)( 97, 98)(100,101)
(103,104)(106,107)(109,110)(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);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope