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The Archimedean duals in general have many stellations. The following table extracted from Webb gives a partial enumeration. In the table, E denotes counts of enantiomorphous ...

Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

A pyritohedron is an irregular dodecahedron composed of identical irregular pentagons. The name "pyritohedron" derives from that fact that a common crystal form in pyrite has ...

The great icosahedron, not to be confused with the great icosidodecahedron orgreat icosicosidodecahedron, is the Kepler-Poinsot polyhedronhose dual is the great stellated ...

The convex hulls of the small cubicuboctahedron U_(13), small rhombihexahedron U_(18), and stellated truncated hexahedron U_(19) are all the Archimedean small ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

A number of attractive tetrahedron 5-compounds can be constructed. The first (left figures) is one of the icosahedron stellations in which the 5×4 vertices of the tetrahedra ...