Polytope of Type {2,12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,136347)
Rank : 5
Schlafli Type : {2,12,6,4}
Number of vertices, edges, etc : 2, 12, 36, 12, 4
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 : {2,12,6,2}*576a, {2,6,6,4}*576a
3-fold quotients : {2,12,2,4}*384, {2,4,6,4}*384a
4-fold quotients : {2,6,6,2}*288a
6-fold quotients : {2,12,2,2}*192, {2,2,6,4}*192a, {2,4,6,2}*192a, {2,6,2,4}*192
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,3,2,4}*96, {2,2,6,2}*96, {2,6,2,2}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
24-fold quotients : {2,2,3,2}*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 := ( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)( 25, 28)
( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 57)( 40, 58)( 41, 59)( 42, 63)
( 43, 64)( 44, 65)( 45, 60)( 46, 61)( 47, 62)( 48, 66)( 49, 67)( 50, 68)
( 51, 72)( 52, 73)( 53, 74)( 54, 69)( 55, 70)( 56, 71)( 78, 81)( 79, 82)
( 80, 83)( 87, 90)( 88, 91)( 89, 92)( 96, 99)( 97,100)( 98,101)(105,108)
(106,109)(107,110)(111,129)(112,130)(113,131)(114,135)(115,136)(116,137)
(117,132)(118,133)(119,134)(120,138)(121,139)(122,140)(123,144)(124,145)
(125,146)(126,141)(127,142)(128,143);;
s2 := ( 3, 42)( 4, 44)( 5, 43)( 6, 39)( 7, 41)( 8, 40)( 9, 45)( 10, 47)
( 11, 46)( 12, 51)( 13, 53)( 14, 52)( 15, 48)( 16, 50)( 17, 49)( 18, 54)
( 19, 56)( 20, 55)( 21, 60)( 22, 62)( 23, 61)( 24, 57)( 25, 59)( 26, 58)
( 27, 63)( 28, 65)( 29, 64)( 30, 69)( 31, 71)( 32, 70)( 33, 66)( 34, 68)
( 35, 67)( 36, 72)( 37, 74)( 38, 73)( 75,123)( 76,125)( 77,124)( 78,120)
( 79,122)( 80,121)( 81,126)( 82,128)( 83,127)( 84,114)( 85,116)( 86,115)
( 87,111)( 88,113)( 89,112)( 90,117)( 91,119)( 92,118)( 93,141)( 94,143)
( 95,142)( 96,138)( 97,140)( 98,139)( 99,144)(100,146)(101,145)(102,132)
(103,134)(104,133)(105,129)(106,131)(107,130)(108,135)(109,137)(110,136);;
s3 := ( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)
( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)( 48, 49)
( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)( 72, 73)
( 75, 85)( 76, 84)( 77, 86)( 78, 88)( 79, 87)( 80, 89)( 81, 91)( 82, 90)
( 83, 92)( 93,103)( 94,102)( 95,104)( 96,106)( 97,105)( 98,107)( 99,109)
(100,108)(101,110)(111,121)(112,120)(113,122)(114,124)(115,123)(116,125)
(117,127)(118,126)(119,128)(129,139)(130,138)(131,140)(132,142)(133,141)
(134,143)(135,145)(136,144)(137,146);;
s4 := ( 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);;
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*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)
( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 39, 57)( 40, 58)( 41, 59)
( 42, 63)( 43, 64)( 44, 65)( 45, 60)( 46, 61)( 47, 62)( 48, 66)( 49, 67)
( 50, 68)( 51, 72)( 52, 73)( 53, 74)( 54, 69)( 55, 70)( 56, 71)( 78, 81)
( 79, 82)( 80, 83)( 87, 90)( 88, 91)( 89, 92)( 96, 99)( 97,100)( 98,101)
(105,108)(106,109)(107,110)(111,129)(112,130)(113,131)(114,135)(115,136)
(116,137)(117,132)(118,133)(119,134)(120,138)(121,139)(122,140)(123,144)
(124,145)(125,146)(126,141)(127,142)(128,143);
s2 := Sym(146)!( 3, 42)( 4, 44)( 5, 43)( 6, 39)( 7, 41)( 8, 40)( 9, 45)
( 10, 47)( 11, 46)( 12, 51)( 13, 53)( 14, 52)( 15, 48)( 16, 50)( 17, 49)
( 18, 54)( 19, 56)( 20, 55)( 21, 60)( 22, 62)( 23, 61)( 24, 57)( 25, 59)
( 26, 58)( 27, 63)( 28, 65)( 29, 64)( 30, 69)( 31, 71)( 32, 70)( 33, 66)
( 34, 68)( 35, 67)( 36, 72)( 37, 74)( 38, 73)( 75,123)( 76,125)( 77,124)
( 78,120)( 79,122)( 80,121)( 81,126)( 82,128)( 83,127)( 84,114)( 85,116)
( 86,115)( 87,111)( 88,113)( 89,112)( 90,117)( 91,119)( 92,118)( 93,141)
( 94,143)( 95,142)( 96,138)( 97,140)( 98,139)( 99,144)(100,146)(101,145)
(102,132)(103,134)(104,133)(105,129)(106,131)(107,130)(108,135)(109,137)
(110,136);
s3 := Sym(146)!( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)
( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)
( 48, 49)( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)
( 72, 73)( 75, 85)( 76, 84)( 77, 86)( 78, 88)( 79, 87)( 80, 89)( 81, 91)
( 82, 90)( 83, 92)( 93,103)( 94,102)( 95,104)( 96,106)( 97,105)( 98,107)
( 99,109)(100,108)(101,110)(111,121)(112,120)(113,122)(114,124)(115,123)
(116,125)(117,127)(118,126)(119,128)(129,139)(130,138)(131,140)(132,142)
(133,141)(134,143)(135,145)(136,144)(137,146);
s4 := 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);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope