Polytope of Type {2,3,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {2,3,6,12}
Number of vertices, edges, etc : 2, 4, 12, 48, 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 : {2,3,6,6}*576
3-fold quotients : {2,3,6,4}*384
6-fold quotients : {2,3,6,2}*192
12-fold quotients : {2,3,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)
( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)
( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)
(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)
(131,143)(132,145)(133,144)(134,146);;
s2 := ( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)( 10, 21)
( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)( 39, 51)
( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)( 47, 59)
( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)( 76, 88)
( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)( 84, 96)
( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)(113,126)
(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)(121,134)
(122,133)(137,138)(141,142)(145,146);;
s3 := ( 3, 6)( 7, 14)( 8, 12)( 9, 13)( 10, 11)( 15, 30)( 16, 28)( 17, 29)
( 18, 27)( 19, 38)( 20, 36)( 21, 37)( 22, 35)( 23, 34)( 24, 32)( 25, 33)
( 26, 31)( 39, 42)( 43, 50)( 44, 48)( 45, 49)( 46, 47)( 51, 66)( 52, 64)
( 53, 65)( 54, 63)( 55, 74)( 56, 72)( 57, 73)( 58, 71)( 59, 70)( 60, 68)
( 61, 69)( 62, 67)( 75,114)( 76,112)( 77,113)( 78,111)( 79,122)( 80,120)
( 81,121)( 82,119)( 83,118)( 84,116)( 85,117)( 86,115)( 87,138)( 88,136)
( 89,137)( 90,135)( 91,146)( 92,144)( 93,145)( 94,143)( 95,142)( 96,140)
( 97,141)( 98,139)( 99,126)(100,124)(101,125)(102,123)(103,134)(104,132)
(105,133)(106,131)(107,130)(108,128)(109,129)(110,127);;
s4 := ( 3, 79)( 4, 80)( 5, 81)( 6, 82)( 7, 75)( 8, 76)( 9, 77)( 10, 78)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)( 18, 94)
( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)( 42,118)
( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)( 66,142)
( 67,135)( 68,136)( 69,137)( 70,138)( 71,143)( 72,144)( 73,145)( 74,146);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
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)!( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)
( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)
( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)
(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)
(130,142)(131,143)(132,145)(133,144)(134,146);
s2 := Sym(146)!( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)
( 10, 21)( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)
( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)
( 47, 59)( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)
( 76, 88)( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)
( 84, 96)( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)
(113,126)(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)
(121,134)(122,133)(137,138)(141,142)(145,146);
s3 := Sym(146)!( 3, 6)( 7, 14)( 8, 12)( 9, 13)( 10, 11)( 15, 30)( 16, 28)
( 17, 29)( 18, 27)( 19, 38)( 20, 36)( 21, 37)( 22, 35)( 23, 34)( 24, 32)
( 25, 33)( 26, 31)( 39, 42)( 43, 50)( 44, 48)( 45, 49)( 46, 47)( 51, 66)
( 52, 64)( 53, 65)( 54, 63)( 55, 74)( 56, 72)( 57, 73)( 58, 71)( 59, 70)
( 60, 68)( 61, 69)( 62, 67)( 75,114)( 76,112)( 77,113)( 78,111)( 79,122)
( 80,120)( 81,121)( 82,119)( 83,118)( 84,116)( 85,117)( 86,115)( 87,138)
( 88,136)( 89,137)( 90,135)( 91,146)( 92,144)( 93,145)( 94,143)( 95,142)
( 96,140)( 97,141)( 98,139)( 99,126)(100,124)(101,125)(102,123)(103,134)
(104,132)(105,133)(106,131)(107,130)(108,128)(109,129)(110,127);
s4 := Sym(146)!( 3, 79)( 4, 80)( 5, 81)( 6, 82)( 7, 75)( 8, 76)( 9, 77)
( 10, 78)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)
( 18, 94)( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)
( 42,118)( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)
( 58,126)( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)
( 66,142)( 67,135)( 68,136)( 69,137)( 70,138)( 71,143)( 72,144)( 73,145)
( 74,146);
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,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
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