Polytope of Type {10,6}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240997)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 160, 480, 96
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,6}*960
16-fold quotients : {10,3}*120a
32-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 2.
48 facets:
48 of {10}*20
80 vertex figures:
80 of {6}*12
P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 2.
48 facets:
48 of {10}*20
80 vertex figures:
80 of {6}*12
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 2.
48 facets:
48 of {10}*20
88 vertex figures:
72 of {6}*12
16 of {3}*6
P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
32 facets:
32 of {10}*20
56 vertex figures:
52 of {6}*12
4 of {2}*4
P/N, where N=<s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 4.
24 facets:
24 of {10}*20
52 vertex figures:
24 of {3}*6
28 of {6}*12
P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2> of order 4.
24 facets:
24 of {10}*20
44 vertex figures:
36 of {6}*12
8 of {3}*6
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
24 facets:
24 of {10}*20
44 vertex figures:
36 of {6}*12
8 of {3}*6
P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1> of order 4.
24 facets:
24 of {10}*20
48 vertex figures:
32 of {6}*12
16 of {3}*6
P/N, where N=<s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1> of order 8.
12 facets:
12 of {10}*20
32 vertex figures:
24 of {3}*6
8 of {6}*12
P/N, where N=<s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2> of order 8.
12 facets:
12 of {10}*20
28 vertex figures:
16 of {3}*6
12 of {6}*12
P/N, where N=<s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 12.
8 facets:
8 of {10}*20
20 vertex figures:
8 of {3}*6
8 of {6}*12
4 of {2}*4
Permutation Representation (GAP) :
s0 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10);;
s1 := (1,3)(2,4)(5,6)(7,8);;
s2 := ( 3,10)( 4, 9)( 5, 8)( 6, 7);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(10)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10);
s1 := Sym(10)!(1,3)(2,4)(5,6)(7,8);
s2 := Sym(10)!( 3,10)( 4, 9)( 5, 8)( 6, 7);
poly := sub<Sym(10)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 >;
References : None.
to this polytope
Twisty Puzzle