You only need to implement truncate and dual operators for the shape you are looking for.įirst some analysis of the image in the question: the spherical triangle spanned by neighbouring pentagon centers seems to be equilateral. such as winged-edge or half-edge datastructures for your mesh. I would suggest using a datastructure that makes it easy to traverse the neighbourhood give a vertex, edge etc. You can already see where this is going.Īpply steps 3 & 4 repeatedly until you are satisfied.įor example below is the mesh for dtdtdtdtI. At this point the recipe is tdtI (read from right!). ![]() We apply the "Dual" operator (Conway notation d). We apply a "Truncate" operation (Conway notation t) to the mesh (the sperical mapping of this one is a football). The polyhedron you are looking for can be generated from an icosahedron - Initialise a mesh with an icosahedron. The construction is easy to follow step by step, you can click the images below to get a live preview. ![]() The ( rather elegant) algorithm to generate this (and many many more) can be succinctly encoded in something called a Conway Polyhedron Notation. The shape you have is one of so called "Goldberg polyhedra", is also a geodesic polyhedra.
0 Comments
Leave a Reply. |