Re: [tuning] Digest Number 944

Dave,

>point
>pt, triangle, triangle, pt
>pt, tetrahedron, octahedron, tetrahedron pt
>pt, 4-simplex, edge-dual of 4-simplex, edge-dual of 4-simplex, 4-simplex, pt
>pt, 5-simplex, edge-dual of 5-simplex, face-dual of 5-simplex, edge-dual of
>5-simplex, 5-simplex, pt
>pt, 6-simplex, edge-dual of 6-simplex, face-dual of 6-simplex, cell-dual of
>6-simplex, face-dual of 6-simplex, edge-dual of 6-simplex, 6-simplex, pt

Yes inded, the "centre" is superfluous, and cell is the better word. A mathematician
would read this description and know straight away what it means.

I called it a truncated simplex because that is what it is called in a number of
web sites such as the java applet page, could equally be called edge-dual of 4-simplex.

I've just done a web search in google for dispentachoron and turned up this page, which
indeed lists it as the dekany:

http://members.aol.com/Polycell/section1.html

It also lists the truncated simplex as another figure, not the edge-dual (as it was on another site)
but the result of more normal truncation in by a third of the length of an edge.
(= five tetrahedra and five truncated tetrahedra
Truncated tetrahedron models:
http://www.georgehart.com/virtual-polyhedra/vrml/truncated_tetrahedron.wrl
(vrml)
http://www.math.umn.edu/~roberts/java.dir/JGV/trunc_tetra1.html
(java)
)

So edge-dual of 4-simplex is clearer.

It also turned up this web page about new naming conventions developed during search for the uniform Polchora.
http://members.aol.com/Polycell/names.html

Robert