Re: -- polyhedron with non-convex faces

In article <slrngr2u7r.c79.tim@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Tim Little <tim@xxxxxxxxxxxxxxxxxx> wrote:

On 2009-03-06, Brian Chandler <imaginatorium@xxxxxxxxxxxxx> wrote:
Ingenious! But it seems slightly unsatisfactory for the polyhedron to
be a torus (topologically).

Well, yes. It was just the first example I thought of.


So I _think_ this is a decahedron with six "dart" faces, two
double-dimpled triangles and two single-dimpled triangles.

Yes, that would certainly work. Or for more symmetry, do the same to
opposite vertices of a cube.

I'm sure I remember seeing a model of intersecting tetrahedra
somewhere, having only *congruent* non-convex faces. ... Aha!

http://en.wikipedia.org/wiki/File:Compound_of_five_tetrahedra.png

Five cubes.

<http://en.wikipedia.org/wiki/File:UC09-5_cubes.png>

These compounds have convex faces.

Here is a (regular) polyhedron with non-convex faces.

<http://en.wikipedia.org/wiki/File:Great_stellated_dodecahedron.png>

--
Michael Press
.

Relevant Pages

  • Re: -- polyhedron with non-convex faces
    ... double-dimpled triangles and two single-dimpled triangles. ... opposite vertices of a cube. ... These compounds have convex faces. ... model of these polyhedra. ...
    (sci.math)
  • Re: -- polyhedron with non-convex faces
    ... double-dimpled triangles and two single-dimpled triangles. ... opposite vertices of a cube. ... These compounds have convex faces. ... model of these polyhedra. ...
    (sci.math)
  • Re: Polyhedra with congruent faces
    ... to find a polyhedron combinatorially equivalent to the cube ... with non-convex faces and intersecting edges. ... expressions for the lengths and angles. ...
    (sci.math)
  • Re: -- polyhedron with non-convex faces
    ... be a torus. ... double-dimpled triangles and two single-dimpled triangles. ... Aha! ...
    (sci.math)