Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2020
|
| Online Access: | https://doi.org/10.5281/zenodo.18000083 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p>his paper presents a mathematical analysis and derives closed-form analytical expressions for the geometric properties of a rhombic dodecahedron. The rhombic dodecahedron is a convex polyhedron consisting of 12 congruent rhombic faces, 24 edges, and 14 vertices. Among these vertices, six identical vertices lie on a common circumscribed sphere of a given radius, while the remaining eight identical vertices do not lie on the same sphere, indicating that the polyhedron is not vertex-transitive. At six vertices, four edges meet, whereas at the remaining eight vertices only three edges intersect. All twelve rhombic faces are located at an equal normal distance from the center of the polyhedron. The rhombic dodecahedron is the dual of the cuboctahedron, an Archimedean solid, and therefore belongs to the class of Catalan solids. It can be geometrically constructed by assembling twelve congruent right pyramids with rhombic bases. Using HCR’s Theory of Polygon, analytical formulas are derived for the face angles and diagonals, the radii of the circumscribed and inscribed spheres, and the surface area and volume of the rhombic dodecahedron, all expressed explicitly in terms of the edge length.</p>