Generate Platonic solids, Archimedian solids, Catalan polyhedra, the trapezohedron, and some stellated polyhedra. You can also stellate any of the polyhedra, select polyhedra by their characterics and ...

It is your responsibility to ensure that the resulting polyhedron is free from self-intersections ... The "tangent" method generally produces good results when connecting a discrete polygon to a ...

Years ago Domokos developed a mathematical tool for describing tessellations based on their average properties rather than ...

a sheet of paper. The two-dimensional space of positive curvature is a convex surface, such as the shell of an egg. It is bent away from the plane towards ...

Not to be confused with Edge (graph theory).

A ring of four squares and four equilateral triangles is below top square and another such ring is above bottom square. An additional ring of eight squares around is center. Hence the model has a ...

Besides Thurston’s paper, I recommend these others: P. Engel and P. Smillie, The number of convex tilings of the sphere by triangles, squares, or hexagons. R. E. Schwartz, Notes on shapes of polyhedra ...

Thurston’s paper Shapes of polyhedra and triangulations of the sphere is really remarkable. I’m writing about it in my next column for the Notices of the American Mathematical Society. Here’s a draft ...

In this way it is possible to follow the development of the disease, to see the crystal-like polyhedra as they are formed in situ and to observe the fine structure of their contents.

Textbooks Lectures are intended to be self-contained. For supplementary readings, with each lecture, we will have pointers to chapters from the following books: ...