 |
 |
Geometry |
|
Authors: Miquel Piñol
We introduce a class of geometric bodies, which we call vertex-edge-combinatorial polytopes, defined by a local structure in which each vertex is connected to a number of edges equal to the dimension of the body, and where any subset of those edges belongs to a face whose dimension equals the subset’s cardinality. These polytopes satisfy an empirical formula for the number of vertices, from which a general combinatorial expression for the number of faces can be deduced. The class includes simplices, hypercubes, and the dodecahedron, and excludes the octahedron, the icosahedron, and any higher-dimensional polytopes derived from them. In some cases where the formula diverges, such as the hexagonal tiling, an infinite regular structure does exist, although this is not always the case.
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Download: PDF
[v1] 2025-05-28 20:30:24
Unique-IP document downloads: 176 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|