id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-028751-71bf4w44	Betten, Anton	Classifying Simplicial Dissections of Convex Polyhedra with Symmetry	2020-06-06		.txt	text/plain	1762	130	62	A convex polyhedron is the convex hull of a finite set of points in [Formula: see text] A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. We present an algorithm to classify the simplicial dissections of a regular polyhedron under the symmetry group of the prolyhedron. The classification algorithm utilizes the concept of a partially ordered set under a group action, using the theory developed by Plesken [9] as a framework. The number of equivalence classes of simplicial dissections of the cube under its automorphism group of order 48 is exactly 10. By using Nauty to solve the isomorphism problem for the associated graphs, the combinatorial objects at hand are classified as well. The poset of orbits for the action of the group of the cube on the partial dissections is shown in Fig. 3 .	./cache/cord-028751-71bf4w44.txt	./txt/cord-028751-71bf4w44.txt