Polytope of Type {20,3}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,3}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5848)
Rank : 3
Schlafli Type : {20,3}
Number of vertices, edges, etc : 240, 360, 36
Order of s0s1s2 : 15
Order of s0s1s2s1 : 20
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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) :
4-fold quotients : {10,3}*360
12-fold quotients : {10,3}*120b
24-fold quotients : {5,3}*60
60-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
24 facets:
12 of {20}*40
12 of {10}*20
120 vertex figures:
120 of {3}*6
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 2.
18 facets:
18 of {20}*40
120 vertex figures:
120 of {3}*6
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
18 facets:
18 of {20}*40
120 vertex figures:
120 of {3}*6
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2> of order 3.
12 facets:
12 of {20}*40
80 vertex figures:
80 of {3}*6
P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 3.
12 facets:
12 of {20}*40
80 vertex figures:
80 of {3}*6
P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
18 facets:
6 of {20}*40
12 of {5}*10
60 vertex figures:
60 of {3}*6
P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1, s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 4.
12 facets:
6 of {20}*40
6 of {10}*20
60 vertex figures:
60 of {3}*6
P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
9 facets:
9 of {20}*40
60 vertex figures:
60 of {3}*6
P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 5.
12 facets:
6 of {20}*40
6 of {4}*8
48 vertex figures:
48 of {3}*6
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 6.
6 facets:
6 of {20}*40
40 vertex figures:
40 of {3}*6
P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 6.
6 facets:
6 of {20}*40
40 vertex figures:
40 of {3}*6
P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 6.
8 facets:
4 of {20}*40
4 of {10}*20
40 vertex figures:
40 of {3}*6
P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 10.
6 facets:
3 of {4}*8
3 of {20}*40
24 vertex figures:
24 of {3}*6
P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 10.
8 facets:
2 of {20}*40
2 of {4}*8
2 of {10}*20
2 of {2}*4
24 vertex figures:
24 of {3}*6
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 12.
3 facets:
3 of {20}*40
20 vertex figures:
20 of {3}*6
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(7,8);;
s2 := (2,5)(3,4)(8,9);;
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,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2,
s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(9)!(1,2)(3,4)(7,8);
s2 := Sym(9)!(2,5)(3,4)(8,9);
poly := sub<Sym(9)|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, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2,
s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope
Twisty Puzzle