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}*1152b
if this polytope has a name.
Group : SmallGroup(1152,136347)
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 : {2,2,6,12}*576a, {2,4,6,6}*576a
3-fold quotients : {2,4,2,12}*384, {2,4,6,4}*384a
4-fold quotients : {2,2,6,6}*288a
6-fold quotients : {2,2,2,12}*192, {2,2,6,4}*192a, {2,4,2,6}*192, {2,4,6,2}*192a
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96, {2,2,6,2}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
24-fold quotients : {2,2,2,3}*48, {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)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 75, 84)( 76, 86)( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)( 82, 92)
( 83, 91)( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)
(100,110)(101,109)(111,120)(112,122)(113,121)(114,123)(115,125)(116,124)
(117,126)(118,128)(119,127)(129,138)(130,140)(131,139)(132,141)(133,143)
(134,142)(135,144)(136,146)(137,145);;
s3 := ( 3, 40)( 4, 39)( 5, 41)( 6, 46)( 7, 45)( 8, 47)( 9, 43)( 10, 42)
( 11, 44)( 12, 49)( 13, 48)( 14, 50)( 15, 55)( 16, 54)( 17, 56)( 18, 52)
( 19, 51)( 20, 53)( 21, 58)( 22, 57)( 23, 59)( 24, 64)( 25, 63)( 26, 65)
( 27, 61)( 28, 60)( 29, 62)( 30, 67)( 31, 66)( 32, 68)( 33, 73)( 34, 72)
( 35, 74)( 36, 70)( 37, 69)( 38, 71)( 75,121)( 76,120)( 77,122)( 78,127)
( 79,126)( 80,128)( 81,124)( 82,123)( 83,125)( 84,112)( 85,111)( 86,113)
( 87,118)( 88,117)( 89,119)( 90,115)( 91,114)( 92,116)( 93,139)( 94,138)
( 95,140)( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)(102,130)
(103,129)(104,131)(105,136)(106,135)(107,137)(108,133)(109,132)(110,134);;
s4 := ( 3, 6)( 4, 7)( 5, 8)( 12, 15)( 13, 16)( 14, 17)( 21, 24)( 22, 25)
( 23, 26)( 30, 33)( 31, 34)( 32, 35)( 39, 60)( 40, 61)( 41, 62)( 42, 57)
( 43, 58)( 44, 59)( 45, 63)( 46, 64)( 47, 65)( 48, 69)( 49, 70)( 50, 71)
( 51, 66)( 52, 67)( 53, 68)( 54, 72)( 55, 73)( 56, 74)( 75, 78)( 76, 79)
( 77, 80)( 84, 87)( 85, 88)( 86, 89)( 93, 96)( 94, 97)( 95, 98)(102,105)
(103,106)(104,107)(111,132)(112,133)(113,134)(114,129)(115,130)(116,131)
(117,135)(118,136)(119,137)(120,141)(121,142)(122,143)(123,138)(124,139)
(125,140)(126,144)(127,145)(128,146);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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)!( 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)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 75, 84)( 76, 86)( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)
( 82, 92)( 83, 91)( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)
( 99,108)(100,110)(101,109)(111,120)(112,122)(113,121)(114,123)(115,125)
(116,124)(117,126)(118,128)(119,127)(129,138)(130,140)(131,139)(132,141)
(133,143)(134,142)(135,144)(136,146)(137,145);
s3 := Sym(146)!( 3, 40)( 4, 39)( 5, 41)( 6, 46)( 7, 45)( 8, 47)( 9, 43)
( 10, 42)( 11, 44)( 12, 49)( 13, 48)( 14, 50)( 15, 55)( 16, 54)( 17, 56)
( 18, 52)( 19, 51)( 20, 53)( 21, 58)( 22, 57)( 23, 59)( 24, 64)( 25, 63)
( 26, 65)( 27, 61)( 28, 60)( 29, 62)( 30, 67)( 31, 66)( 32, 68)( 33, 73)
( 34, 72)( 35, 74)( 36, 70)( 37, 69)( 38, 71)( 75,121)( 76,120)( 77,122)
( 78,127)( 79,126)( 80,128)( 81,124)( 82,123)( 83,125)( 84,112)( 85,111)
( 86,113)( 87,118)( 88,117)( 89,119)( 90,115)( 91,114)( 92,116)( 93,139)
( 94,138)( 95,140)( 96,145)( 97,144)( 98,146)( 99,142)(100,141)(101,143)
(102,130)(103,129)(104,131)(105,136)(106,135)(107,137)(108,133)(109,132)
(110,134);
s4 := Sym(146)!( 3, 6)( 4, 7)( 5, 8)( 12, 15)( 13, 16)( 14, 17)( 21, 24)
( 22, 25)( 23, 26)( 30, 33)( 31, 34)( 32, 35)( 39, 60)( 40, 61)( 41, 62)
( 42, 57)( 43, 58)( 44, 59)( 45, 63)( 46, 64)( 47, 65)( 48, 69)( 49, 70)
( 50, 71)( 51, 66)( 52, 67)( 53, 68)( 54, 72)( 55, 73)( 56, 74)( 75, 78)
( 76, 79)( 77, 80)( 84, 87)( 85, 88)( 86, 89)( 93, 96)( 94, 97)( 95, 98)
(102,105)(103,106)(104,107)(111,132)(112,133)(113,134)(114,129)(115,130)
(116,131)(117,135)(118,136)(119,137)(120,141)(121,142)(122,143)(123,138)
(124,139)(125,140)(126,144)(127,145)(128,146);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope