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A one-dimensional line segment where two two-dimensional faces of an n-dimensional polytope meet, also called a side.

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...

The curve with trilinear coordinates a^t:b^t:c^t for a given power t.

Let DeltaA^'B^'C^' be the reflection of the orthic triangle of the reference triangle DeltaABC in the nine-point center. Then DeltaA^'B^'C^' and DeltaABC are in perspective, ...

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

At each point on a given a two-dimensional surface, there are two "principal" radii of curvature. The larger is denoted R_1, and the smaller R_2. The "principal directions" ...

A polygon vertex x_i of a simple polygon P is a principal polygon vertex if the diagonal [x_(i-1),x_(i+1)] intersects the boundary of P only at x_(i-1) and x_(i+1).

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.

A prismatoid having planar sides and the same number of vertices in both of its parallel planes. The faces of a prismoid are therefore either trapezoids or parallelograms. ...

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...