Name
Abstract | ||
|---|---|---|
Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a suitable rotation) all faces are perpendicular to a coordinate axis, and hence all edges are parallel to a coordinate axis. Clearly, any facial angle and any dihedral angle is a multiple of $\pi/2$. In this note we explore the converse: if the facial and/or dihedral angles are all multiples of $\pi /2$, is the polyhedron necessarily orthogonal? The case of facial angles was answered previously. In this note we show that if both the facial and dihedral angles are multiples of $\pi /2$ then the polyhedron is orthogonal (presuming connectivity), and we give examples to show that the condition for dihedral angles alone does not suffice. |
Year | Venue | Field |
|---|---|---|
2013 | CoRR | Converse,Perpendicular,Combinatorics,Vertex (geometry),Spherical angle,Polyhedron,Geometry,Mathematics,Dihedral angle |
DocType | Volume | Citations |
Journal | abs/1312.6824 | 0 |
PageRank | References | Authors |
0.34 | 2 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Therese Biedl | 1 | 902 | 106.36 |
| Martin Derka | 2 | 5 | 5.96 |
| Stephen Kiazyk | 3 | 4 | 1.45 |
| Anna Lubiw | 4 | 753 | 95.36 |
| Hamide Vosoughpour | 5 | 9 | 2.26 |