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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 ...

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

The intersection Ev of the Gergonne line and the Euler line. It has triangle center function alpha=(b(a-b+c)cosB+c(a+b-c)cosC-2a^2cosA)/(2a) and is Kimberling center X_(1375).

The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles (P. Moses, pers. comm., Jan. 29, 2005). It has center at the ...

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 ...

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

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

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.