three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather than...

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive...

geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices. The word circumsphere...

surfaces is the Kleinian model. Dini's surface Hyperbolic 3-manifold Ideal polyhedron Mostow rigidity theorem Murakami–Yano formula Pseudosphere Grigor'yan...

or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform...

approach it). In the hyperboloid model there are no ideal points. Ideal triangle Ideal polyhedron Points at infinity for uses in other geometries. Sibley...

surface of a polyhedron is called its development. The polyhedron can be thought of as being folded from a sheet of paper (a net for the polyhedron) and it...

to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another, and whether a polyhedron or its dissections can tile...

convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this...