1. Stellations program
The main purpose of the applet is to create a computer program for finding the stellations of polyhedra. As an example, uses the applet 5. Three-parameter model transformations of the Dodecahedron faces. The input data is a matrix of vertex numbers for all faces: m4-quadrilaterals, m6-hexagons, and m10-decagons.
You need to find all the n-polygons of the polyhedron that are parallel to the corresponding faces of n-polygons. For each quadrilateral face, there are -15, -11 for the hexagon face, and -7 different flat polygons for the decagon face. Intersection of all polygons with the same ordinal define their star-shaped structure. For example, the k4 -slider sorts star-shaped structures "generated" by a quadrilateral face. For different parameters t and q, by choosing different combinations of sliders (k4,k6, k10), you can get different structures. In the applet, I selected 92 cases, among which there are many known structures.
To calculate a another structure, click the delete "del S" matrices button in the section "delete matrix s n:i=1..20", specify the types: n-gons={3,5,...} of faces in the list, and then for the corresponding faces matrices: m3, m5,... you can calculate the stellation matrices.
All applets for creation of polyhedra Stellations("Internal"). Truncated icosidodecahedron:
1. Stellations program.
2. Method of Creation of stellations using as an example of three-parameter model of an Truncated icosidodecahedron.
3. Construction of quadrilaterals with vertices symmetric with respect to the centroid of the origin polyhedron.
4. Images. Construction of quadrilaterals with vertices symmetric with respect to the centroid of the origin polyhedron.
5. 92 Stellations with example of model of an Truncated icosidodecahedron.
6. Images of 92 Stellations with example of model of an Truncated icosidodecahedron.