Acute Triangulations of the Cuboctahedral Surface
Xiao Feng, Liping Yuan
TL;DR
This paper proves that the surface of the cuboctahedron can be optimally triangulated into 8 non-obtuse and 12 acute triangles, establishing the best possible bounds for such triangulations.
Contribution
It provides the first known optimal triangulations of the cuboctahedral surface into acute and non-obtuse triangles, with proofs of minimal bounds.
Findings
Surface can be triangulated into 8 non-obtuse triangles
Surface can be triangulated into 12 acute triangles
Both bounds are proven to be optimal
Abstract
In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the best possible.
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Graph Labeling and Dimension Problems