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The Stammler circles are the three circles (apart from the circumcircle), that intercept the sidelines of a reference triangle DeltaABC in chords of lengths equal to the ...

The stellated truncated hexahedron (Maeder 1997), also called the quasitruncated hexahedron (Wenninger 1989, p. 144), is the uniform polyhedron with Maeder index 19 (Maeder ...

Synergetics coordinates are a set of triangular coordinates in their plane (or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions). ...

The tangential mid-arc triangle of a reference triangle DeltaABC is the triangle DeltaA^'B^'C^' whose sides are the tangents to the incircle at the intersections of the ...

A toroidal polyhedron is a polyhedron with genus g>=1 (i.e., one having one or more holes). Examples of toroidal polyhedra include the Császár polyhedron and Szilassi ...

A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new ...

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...