Polytope of Type {2,2,12,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,6,3}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30782)
Rank : 6
Schlafli Type : {2,2,12,6,3}
Number of vertices, edges, etc : 2, 2, 12, 36, 9, 3
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,6,6,3}*864a
3-fold quotients : {2,2,12,2,3}*576
4-fold quotients : {2,2,3,6,3}*432
6-fold quotients : {2,2,6,2,3}*288
9-fold quotients : {2,2,4,2,3}*192
12-fold quotients : {2,2,3,2,3}*144
18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9, 10)( 12, 13)( 14, 23)( 15, 25)( 16, 24)( 17, 26)( 18, 28)
( 19, 27)( 20, 29)( 21, 31)( 22, 30)( 33, 34)( 36, 37)( 39, 40)( 41, 50)
( 42, 52)( 43, 51)( 44, 53)( 45, 55)( 46, 54)( 47, 56)( 48, 58)( 49, 57)
( 59, 86)( 60, 88)( 61, 87)( 62, 89)( 63, 91)( 64, 90)( 65, 92)( 66, 94)
( 67, 93)( 68,104)( 69,106)( 70,105)( 71,107)( 72,109)( 73,108)( 74,110)
( 75,112)( 76,111)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81,100)( 82, 99)
( 83,101)( 84,103)( 85,102);;
s3 := ( 5, 68)( 6, 70)( 7, 69)( 8, 72)( 9, 71)( 10, 73)( 11, 76)( 12, 75)
( 13, 74)( 14, 59)( 15, 61)( 16, 60)( 17, 63)( 18, 62)( 19, 64)( 20, 67)
( 21, 66)( 22, 65)( 23, 77)( 24, 79)( 25, 78)( 26, 81)( 27, 80)( 28, 82)
( 29, 85)( 30, 84)( 31, 83)( 32, 95)( 33, 97)( 34, 96)( 35, 99)( 36, 98)
( 37,100)( 38,103)( 39,102)( 40,101)( 41, 86)( 42, 88)( 43, 87)( 44, 90)
( 45, 89)( 46, 91)( 47, 94)( 48, 93)( 49, 92)( 50,104)( 51,106)( 52,105)
( 53,108)( 54,107)( 55,109)( 56,112)( 57,111)( 58,110);;
s4 := ( 5, 8)( 6, 10)( 7, 9)( 12, 13)( 14, 17)( 15, 19)( 16, 18)( 21, 22)
( 23, 26)( 24, 28)( 25, 27)( 30, 31)( 32, 35)( 33, 37)( 34, 36)( 39, 40)
( 41, 44)( 42, 46)( 43, 45)( 48, 49)( 50, 53)( 51, 55)( 52, 54)( 57, 58)
( 59, 62)( 60, 64)( 61, 63)( 66, 67)( 68, 71)( 69, 73)( 70, 72)( 75, 76)
( 77, 80)( 78, 82)( 79, 81)( 84, 85)( 86, 89)( 87, 91)( 88, 90)( 93, 94)
( 95, 98)( 96,100)( 97, 99)(102,103)(104,107)(105,109)(106,108)(111,112);;
s5 := ( 6, 7)( 8, 11)( 9, 13)( 10, 12)( 15, 16)( 17, 20)( 18, 22)( 19, 21)
( 24, 25)( 26, 29)( 27, 31)( 28, 30)( 33, 34)( 35, 38)( 36, 40)( 37, 39)
( 42, 43)( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 53, 56)( 54, 58)( 55, 57)
( 60, 61)( 62, 65)( 63, 67)( 64, 66)( 69, 70)( 71, 74)( 72, 76)( 73, 75)
( 78, 79)( 80, 83)( 81, 85)( 82, 84)( 87, 88)( 89, 92)( 90, 94)( 91, 93)
( 96, 97)( 98,101)( 99,103)(100,102)(105,106)(107,110)(108,112)(109,111);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(112)!(1,2);
s1 := Sym(112)!(3,4);
s2 := Sym(112)!( 6, 7)( 9, 10)( 12, 13)( 14, 23)( 15, 25)( 16, 24)( 17, 26)
( 18, 28)( 19, 27)( 20, 29)( 21, 31)( 22, 30)( 33, 34)( 36, 37)( 39, 40)
( 41, 50)( 42, 52)( 43, 51)( 44, 53)( 45, 55)( 46, 54)( 47, 56)( 48, 58)
( 49, 57)( 59, 86)( 60, 88)( 61, 87)( 62, 89)( 63, 91)( 64, 90)( 65, 92)
( 66, 94)( 67, 93)( 68,104)( 69,106)( 70,105)( 71,107)( 72,109)( 73,108)
( 74,110)( 75,112)( 76,111)( 77, 95)( 78, 97)( 79, 96)( 80, 98)( 81,100)
( 82, 99)( 83,101)( 84,103)( 85,102);
s3 := Sym(112)!( 5, 68)( 6, 70)( 7, 69)( 8, 72)( 9, 71)( 10, 73)( 11, 76)
( 12, 75)( 13, 74)( 14, 59)( 15, 61)( 16, 60)( 17, 63)( 18, 62)( 19, 64)
( 20, 67)( 21, 66)( 22, 65)( 23, 77)( 24, 79)( 25, 78)( 26, 81)( 27, 80)
( 28, 82)( 29, 85)( 30, 84)( 31, 83)( 32, 95)( 33, 97)( 34, 96)( 35, 99)
( 36, 98)( 37,100)( 38,103)( 39,102)( 40,101)( 41, 86)( 42, 88)( 43, 87)
( 44, 90)( 45, 89)( 46, 91)( 47, 94)( 48, 93)( 49, 92)( 50,104)( 51,106)
( 52,105)( 53,108)( 54,107)( 55,109)( 56,112)( 57,111)( 58,110);
s4 := Sym(112)!( 5, 8)( 6, 10)( 7, 9)( 12, 13)( 14, 17)( 15, 19)( 16, 18)
( 21, 22)( 23, 26)( 24, 28)( 25, 27)( 30, 31)( 32, 35)( 33, 37)( 34, 36)
( 39, 40)( 41, 44)( 42, 46)( 43, 45)( 48, 49)( 50, 53)( 51, 55)( 52, 54)
( 57, 58)( 59, 62)( 60, 64)( 61, 63)( 66, 67)( 68, 71)( 69, 73)( 70, 72)
( 75, 76)( 77, 80)( 78, 82)( 79, 81)( 84, 85)( 86, 89)( 87, 91)( 88, 90)
( 93, 94)( 95, 98)( 96,100)( 97, 99)(102,103)(104,107)(105,109)(106,108)
(111,112);
s5 := Sym(112)!( 6, 7)( 8, 11)( 9, 13)( 10, 12)( 15, 16)( 17, 20)( 18, 22)
( 19, 21)( 24, 25)( 26, 29)( 27, 31)( 28, 30)( 33, 34)( 35, 38)( 36, 40)
( 37, 39)( 42, 43)( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 53, 56)( 54, 58)
( 55, 57)( 60, 61)( 62, 65)( 63, 67)( 64, 66)( 69, 70)( 71, 74)( 72, 76)
( 73, 75)( 78, 79)( 80, 83)( 81, 85)( 82, 84)( 87, 88)( 89, 92)( 90, 94)
( 91, 93)( 96, 97)( 98,101)( 99,103)(100,102)(105,106)(107,110)(108,112)
(109,111);
poly := sub<Sym(112)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope