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A sphere with two handles and two holes, i.e., a genus-2 torus.

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

Given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by e={sqrt((a^2-c^2)/(a^2)) c<a (oblate spheroid); sqrt((c^2-a^2)/(c^2)) c>a (prolate ...

The elongated gyrobifastigium, which could also be called an elongated digonal gyrobicupola, is a family of octahedra obtained by elongating the gyrobifastigium with four ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is ...

An (n-1)-dimensional face of an n-dimensional polytope. A procedure for generating facets is known as faceting.

The flattening of a spheroid (also called oblateness) is denoted epsilon or f (Snyder 1987, p. 13). It is defined as epsilon={(a-c)/a=1-c/a oblate; (c-a)/a=c/a-1 prolate, (1) ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...