Polytope of Type {4,10}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10}*960
if this polytope has a name.
Group : SmallGroup(960,10882)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 48, 240, 120
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Facet Of :
{4,10,2} of size 1920
Vertex Figure Of :
{2,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,10}*480a, {4,10}*480b, {4,10}*480c
4-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
8-fold quotients : {4,5}*120
60-fold quotients : {4,2}*16
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,20}*1920a, {8,10}*1920a, {8,10}*1920b, {4,20}*1920b, {4,10}*1920
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
60 facets:
60 of {4}*8
24 vertex figures:
24 of {10}*20
P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
60 facets:
60 of {4}*8
36 vertex figures:
24 of {5}*10
12 of {10}*20
P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
60 facets:
60 of {4}*8
24 vertex figures:
24 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 2.
64 facets:
56 of {4}*8
8 of {2}*4
24 vertex figures:
24 of {10}*20
P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 3.
40 facets:
40 of {4}*8
16 vertex figures:
16 of {10}*20
P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
30 facets:
30 of {4}*8
12 vertex figures:
12 of {10}*20
P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
34 facets:
8 of {2}*4
26 of {4}*8
12 vertex figures:
12 of {10}*20
P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
32 facets:
28 of {4}*8
4 of {2}*4
18 vertex figures:
12 of {5}*10
6 of {10}*20
P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 5.
24 facets:
24 of {4}*8
16 vertex figures:
8 of {10}*20
8 of {2}*4
P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 6.
20 facets:
20 of {4}*8
8 vertex figures:
8 of {10}*20
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 6.
24 facets:
16 of {4}*8
8 of {2}*4
8 vertex figures:
8 of {10}*20
P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0> of order 10.
12 facets:
12 of {4}*8
8 vertex figures:
4 of {2}*4
4 of {10}*20
P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10.
16 facets:
8 of {2}*4
8 of {4}*8
8 vertex figures:
4 of {10}*20
4 of {2}*4
P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 12.
10 facets:
10 of {4}*8
4 vertex figures:
4 of {10}*20
Permutation Representation (GAP) :
s0 := (3,4)(7,8);;
s1 := (1,3)(2,4)(6,7)(8,9);;
s2 := ( 5, 6)( 7, 8)(10,11);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(11)!(3,4)(7,8);
s1 := Sym(11)!(1,3)(2,4)(6,7)(8,9);
s2 := Sym(11)!( 5, 6)( 7, 8)(10,11);
poly := sub<Sym(11)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope
Twisty Puzzle