add-on Geometry`Polytopes` : Faces
- To: mathgroup@smc.vnet.net
- Subject: [mg11995] add-on Geometry`Polytopes` : Faces
- From: Wouter Meeussen <eu000949@pophost.eunet.be>
- Date: Fri, 17 Apr 1998 03:40:31 -0400
Although I'm not entirely sure,
it is my impression that the Faces of the polytopes Icosahedron and
Dodecahedron are not numbered consistently with those of Cube,
Octahedron and Tetrahedron.
For these last three polytopes, the Faces are circulated in such way as
to have a negative sign (outward pointing surface vector) As is,
the Icosahedron has all inward pointing surface vectors
(positive signs);
the Dodecahedron has all *but*one*face* outward pointing signs.
In my view, the Faces[Icosahedron] should produce:
{{1,2,3},{1,3,4},{1,4,5},{1,5,6},{1,6,2},
{2,6,11},{2,7,3},{2,11,7},{3,7,8},{3,8,4},
{4,8,9},{4,9,5},{5,9,10},{5,10,6},{6,10,11},
{7,11,12},{7,12,8},{8,12,9},{9,12,10},{10,12,11}}
and for the Faces[Dodecahedron]
{{1,2,3,4,5},{1,5,10,15,6},{1,6,11,7,2},{2,7,12,8,3},{3,8,13,9,4},
{4,9,14,10,5},{6,15,20,16,11},{7,11,16,17,12},{8,12,17,18,13},
{9,13,18,19,14},{10,14,19,20,15},{16,20,19,18,17}}
------------------------------------------------------------- My lack of
conviction stems from the way the Dodecahedron (both Vertices & Faces)
is calculated in this package :
^^^^^^^^^^ Dodecahedron/: Faces[Dodecahedron]
:=
Dodecahedron/: Faces[Dodecahedron] =
DualFaces[Icosahedron]
I would be very surprised if an incorrectness in these functions could
result in the near-correct results as they are currently produced.
Please, correct me if I am wrong.
wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc@vandemoortele.be
eu000949@pophost.eunet.be