Sequence: total number of vertices in all n-dimensional regular polytopes

[Andrew Weimholt]

On 7/14/08, Jonathan Post <jvospost3 at gmail.com> wrote:
>
> So, revised title and formula:
>
> Total number of vertices in all finite n-dimensional convex regular
> polytopes, or -1 if the number is infinite.
>
> 1, 2, -1, 106, 2453, 48, 83, 150, 281, 540, ...

I think you meant 1, 2, -1, 50, 773, 48, 83, 150, 281, 540, ...
as you have applied the "convex" restriction.

The title for the alternate sequence can be
"Total number of vertices in all finite n-dimensional regular
polytopes, or -1 if the number is infinite. (includes both convex and
non-convex)"

1, 2, -1, 106, 2453, 48, 83, 150, 281, 540, ...

The sequence of just the non-convex cases is not as interesting, since it's
all zeros from a(5) on...

0, 0, -1, 56, 1680, 0, 0, 0, ,,,

Andrew