Polytope of Type {12,5}
Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,5}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240996)
Rank : 3
Schlafli Type : {12,5}
Number of vertices, edges, etc : 192, 480, 80
Order of s0s1s2 : 4
Order of s0s1s2s1 : 8
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) :
16-fold quotients : {6,5}*120a
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
40 facets:
40 of {12}*24
96 vertex figures:
96 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
44 facets:
36 of {12}*24
8 of {6}*12
96 vertex figures:
96 of {5}*10
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 3.
28 facets:
26 of {12}*24
2 of {4}*8
64 vertex figures:
64 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
26 facets:
14 of {12}*24
12 of {6}*12
48 vertex figures:
48 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
22 facets:
18 of {12}*24
4 of {6}*12
48 vertex figures:
48 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
26 facets:
18 of {12}*24
8 of {3}*6
48 vertex figures:
48 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
24 facets:
16 of {12}*24
8 of {6}*12
48 vertex figures:
48 of {5}*10
P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 8.
16 facets:
4 of {12}*24
12 of {6}*12
24 vertex figures:
24 of {5}*10
P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1, s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 8.
14 facets:
6 of {12}*24
8 of {6}*12
24 vertex figures:
24 of {5}*10
P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1> of order 12.
10 facets:
4 of {12}*24
2 of {4}*8
4 of {6}*12
16 vertex figures:
16 of {5}*10
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5,10)( 6, 7)( 8, 9);;
s1 := ( 1, 5)( 3, 8)( 4,10)( 7, 9);;
s2 := ( 2, 3)( 5, 8)( 6, 7)( 9,10);;
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,
s2*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(10)!( 2, 3)( 5,10)( 6, 7)( 8, 9);
s1 := Sym(10)!( 1, 5)( 3, 8)( 4,10)( 7, 9);
s2 := Sym(10)!( 2, 3)( 5, 8)( 6, 7)( 9,10);
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,
s2*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
to this polytope
Twisty Puzzle