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A pentagonal prisim has 15 edges. 10 of these are base edges and then 5 lateral edges. AnswerParty!

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**heptagonal prism**
**Geometry**
**Euclidean geometry** is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the *Elements*. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The *Elements* begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the *Elements* states results of what are now called algebra and number theory, explained in geometrical language.

For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak.

**Polyhedra**
**Polychora**
**Prism**
A **uniform polyhedron** is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.

Uniform polyhedra may be regular (if also face and edge transitive), quasi-regular (if edge transitive but not face transitive) or semi-regular (if neither edge nor face transitive). The faces and vertices need not be convex, so many of the uniform polyhedra are also star polyhedra.

In 4-dimensional geometry, a **uniform antiprismatic prism** or **antiduoprism** is a uniform polychoron with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces. The symmetry of a *p*-gonal antiprismatic prism is [2p,2+,2], order 8p.

A **p-gonal antiprismatic prism** or **p-gonal antiduoprism** has *4p* triangle, *4p* square and *4* p-gon faces. It has *10p* edges, and *4p* vertices.

**Heptahedron**
**Hospitality** is the relationship between the guest and the host, or the act or practice of being hospitable. This includes the reception and entertainment of guests, visitors, or strangers.