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The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

The polyhedron compound consisting of the cuboctahedron and its dual, the rhombic dodecahedron, illustrated in the left figure above. The right figure shows the solid common ...

A hexecontahedron is a 60-faced polyhedron. Examples include the deltoidal hexecontahedron, rhombic hexecontahedron, and triakis icosahedron. Counting the faces produced by ...

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

The polyhedron compound of the great icosahedron (U_(53)) and the small stellated dodecahedron (U_(34)), sometimes known as the great cid. Four faces meet at each edge of the ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. ...

The "temperature" of a curve Gamma is defined as T=1/(ln((2l)/(2l-h))), where l is the length of Gamma and h is the length of the perimeter of the convex hull. The ...