Geodesic
A Generalized Vertex Truncation Scheme to Construct Intriguing Polyhedral Shapes
In this paper, we present a method to create a new class of polyhedra. All the faces of these polyhedra are bounded by smooth (quadratic B-spline) curves and the face boundaries are C1 discontinuous everywhere. These polyhedral shapes are limit surfaces of a generalized vertex truncation subdivision scheme. We obtain an approximation of these smooth and fractal polyhedra by iteratively applying a new vertex truncation scheme to an initial manifold mesh. Our vertex truncation scheme is based on Chaikin's construction. If the initial manifold mesh is a polyhedra only with planar faces and 3-valent vertices, in each iteration we construct a polyhedral mesh in which all faces are planar and every vertex is 3-valent,
Classification : 52B10 
@article{VM_2005_7_1_a0,
     author = {Ergun Akleman and Paul Edmundson and Ozan Ozener},
     title = {A {Generalized} {Vertex} {Truncation} {Scheme} to    {Construct} {Intriguing} {Polyhedral} {Shapes}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2005_7_1_a0/}
}
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Ergun Akleman; Paul Edmundson; Ozan Ozener. A Generalized Vertex Truncation Scheme to    Construct Intriguing Polyhedral Shapes. Visual Mathematics, Tome 7 (2005) no. 1. http://geodesic.mathdoc.fr/item/VM_2005_7_1_a0/