Sharpohedron

For general discussion of polyhedra, not necessarily Stella-specific.
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marcelteun
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Re: Sharpohedron

Post by marcelteun » Tue Mar 30, 2021 6:19 pm

In some cases where the crosses are on the 2-fold axes it could be a good idea to extend the crosses to obtain regular faces. E.g.
https://tunnissen.eu/polyh/local_off.ht ... istance=25
https://tunnissen.eu/polyh/local_off.ht ... istance=35
https://tunnissen.eu/polyh/local_off.ht ... istance=45

This also gives more options for faceting.

However this opens up a whole new wide range of possibilities. Why not widen the shorter legs in the previous example and extend them until they meet? Then all other faces are equilateral triangles, though of four different sizes. And there are an infinite amount of possibilities for that one.

It seems a good idea to limit the search space to crosses with the following properties:
- the width of the legs are the same
- if seeing the cross as compound of two rectangles, one of these shall have a ratio of 1:3 (i.e. it consists of 3 squares.)

These could be indicated by 1:3:1:n Crossohedra, with the special sub-set 1:3:1:3 for which some were listed below.

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marcelteun
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Re: Sharpohedron

Post by marcelteun » Wed Mar 31, 2021 5:38 pm

Updated the list below:
Renamed
crosso-S4xI_o2o4.off to crosso-S4xI-o2_and_o4.off

Added:
https://tunnissen.eu/polyh/local_off.ht ... stencil=on
https://tunnissen.eu/polyh/local_off.ht ... stencil=on
~

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marcelteun
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Re: Sharpohedron

Post by marcelteun » Wed Mar 31, 2021 9:03 pm


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marcelteun
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Re: Sharpohedron

Post by marcelteun » Thu Apr 01, 2021 5:31 pm

Hi

I created my own web-page about Crossohedra. Then I have all the freedom, e.g. use "Crossohedra" instead of Sharpohedron. The page is here:
https://tunnissen.eu/polyh/crossohedra/list.html
And it is far from complete and needs a lot of work still.
To this page I added a few Crossohedra with prism symmetry

I will stop updating the list on this forum.

/MT

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