Re: Sharpohedron
Posted: 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.
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.