Polytope of Type {2,12,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,6}*1728g
if this polytope has a name.
Group : SmallGroup(1728,47409)
Rank : 5
Schlafli Type : {2,12,6,6}
Number of vertices, edges, etc : 2, 12, 36, 18, 6
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 : {2,6,6,6}*864f
3-fold quotients : {2,4,6,6}*576b, {2,12,6,2}*576c
4-fold quotients : {2,6,3,6}*432
6-fold quotients : {2,2,6,6}*288c, {2,6,6,2}*288b
9-fold quotients : {2,4,6,2}*192a
12-fold quotients : {2,2,3,6}*144, {2,6,3,2}*144
18-fold quotients : {2,2,6,2}*96
27-fold quotients : {2,4,2,2}*64
36-fold quotients : {2,2,3,2}*48
54-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)( 42, 45)( 43, 46)( 44, 47)( 51, 54)
( 52, 55)( 53, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)( 62, 92)
( 63, 87)( 64, 88)( 65, 89)( 66, 93)( 67, 94)( 68, 95)( 69, 99)( 70,100)
( 71,101)( 72, 96)( 73, 97)( 74, 98)( 75,102)( 76,103)( 77,104)( 78,108)
( 79,109)( 80,110)( 81,105)( 82,106)( 83,107);;
s2 := ( 3, 60)( 4, 62)( 5, 61)( 6, 57)( 7, 59)( 8, 58)( 9, 63)( 10, 65)
( 11, 64)( 12, 78)( 13, 80)( 14, 79)( 15, 75)( 16, 77)( 17, 76)( 18, 81)
( 19, 83)( 20, 82)( 21, 69)( 22, 71)( 23, 70)( 24, 66)( 25, 68)( 26, 67)
( 27, 72)( 28, 74)( 29, 73)( 30, 87)( 31, 89)( 32, 88)( 33, 84)( 34, 86)
( 35, 85)( 36, 90)( 37, 92)( 38, 91)( 39,105)( 40,107)( 41,106)( 42,102)
( 43,104)( 44,103)( 45,108)( 46,110)( 47,109)( 48, 96)( 49, 98)( 50, 97)
( 51, 93)( 52, 95)( 53, 94)( 54, 99)( 55,101)( 56,100);;
s3 := ( 3, 13)( 4, 12)( 5, 14)( 6, 19)( 7, 18)( 8, 20)( 9, 16)( 10, 15)
( 11, 17)( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 40)( 31, 39)( 32, 41)
( 33, 46)( 34, 45)( 35, 47)( 36, 43)( 37, 42)( 38, 44)( 48, 49)( 51, 55)
( 52, 54)( 53, 56)( 57, 67)( 58, 66)( 59, 68)( 60, 73)( 61, 72)( 62, 74)
( 63, 70)( 64, 69)( 65, 71)( 75, 76)( 78, 82)( 79, 81)( 80, 83)( 84, 94)
( 85, 93)( 86, 95)( 87,100)( 88, 99)( 89,101)( 90, 97)( 91, 96)( 92, 98)
(102,103)(105,109)(106,108)(107,110);;
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)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)
(100,101)(103,104)(106,107)(109,110);;
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,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(110)!(1,2);
s1 := Sym(110)!( 6, 9)( 7, 10)( 8, 11)( 15, 18)( 16, 19)( 17, 20)( 24, 27)
( 25, 28)( 26, 29)( 33, 36)( 34, 37)( 35, 38)( 42, 45)( 43, 46)( 44, 47)
( 51, 54)( 52, 55)( 53, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 90)( 61, 91)
( 62, 92)( 63, 87)( 64, 88)( 65, 89)( 66, 93)( 67, 94)( 68, 95)( 69, 99)
( 70,100)( 71,101)( 72, 96)( 73, 97)( 74, 98)( 75,102)( 76,103)( 77,104)
( 78,108)( 79,109)( 80,110)( 81,105)( 82,106)( 83,107);
s2 := Sym(110)!( 3, 60)( 4, 62)( 5, 61)( 6, 57)( 7, 59)( 8, 58)( 9, 63)
( 10, 65)( 11, 64)( 12, 78)( 13, 80)( 14, 79)( 15, 75)( 16, 77)( 17, 76)
( 18, 81)( 19, 83)( 20, 82)( 21, 69)( 22, 71)( 23, 70)( 24, 66)( 25, 68)
( 26, 67)( 27, 72)( 28, 74)( 29, 73)( 30, 87)( 31, 89)( 32, 88)( 33, 84)
( 34, 86)( 35, 85)( 36, 90)( 37, 92)( 38, 91)( 39,105)( 40,107)( 41,106)
( 42,102)( 43,104)( 44,103)( 45,108)( 46,110)( 47,109)( 48, 96)( 49, 98)
( 50, 97)( 51, 93)( 52, 95)( 53, 94)( 54, 99)( 55,101)( 56,100);
s3 := Sym(110)!( 3, 13)( 4, 12)( 5, 14)( 6, 19)( 7, 18)( 8, 20)( 9, 16)
( 10, 15)( 11, 17)( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 40)( 31, 39)
( 32, 41)( 33, 46)( 34, 45)( 35, 47)( 36, 43)( 37, 42)( 38, 44)( 48, 49)
( 51, 55)( 52, 54)( 53, 56)( 57, 67)( 58, 66)( 59, 68)( 60, 73)( 61, 72)
( 62, 74)( 63, 70)( 64, 69)( 65, 71)( 75, 76)( 78, 82)( 79, 81)( 80, 83)
( 84, 94)( 85, 93)( 86, 95)( 87,100)( 88, 99)( 89,101)( 90, 97)( 91, 96)
( 92, 98)(102,103)(105,109)(106,108)(107,110);
s4 := Sym(110)!( 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)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)
( 97, 98)(100,101)(103,104)(106,107)(109,110);
poly := sub<Sym(110)|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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >;
to this polytope