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The truncated pentakis dodecahedron is a polyhedron on 180 vertices, 270 edges, and 92 faces. Its canonical polyhedron has edges of three different lengths and faces ...

The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base and top side lengths of the truncated pyramid be a and b, and let the ...

The truncated triangular prism is an undecagon obtained by truncation of a triangular prism. It has 18 vertices, 27 edges, and 11 faces. As a canonical polyhedron with unit ...

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

The three planes determined by the edges of a trihedron and the internal bisectors of the respectively opposite faces are coaxal, and the common line of these planes is ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

A plane making equal angles with the three edges of a trihedron.

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...