5. 92 Stellations with example of model of an Truncated icosidodecahedron.
For different parameters t and q, by choosing different combinations of sliders (k4, k4', k6, k10), you can get different structures. In the applet, I selected 92 cases, among which there are many known structures with a different number of vertexes: V=12, 20, 30, 60, 120.
Using the sliders (k4, k6, k10), it is possible to sort through all polygons with 4-, 6-, 10-vertices that have the following attribute: their planes are at the same distance from the corresponding faces of the origin polyhedron. For each type of polygon, vertices can be traversed in different ways. For example, 5-gon can be represented either as a convex pentagon or as a five-pointed star. In the applet for each type of polygon there are several ways to bypass their vertices. For example, STELlations10(1) ... STELlations10(4).
The slider k4' goes over all the quadrilaterals (there are 1770 for a specific case) whose vertices are symmetrical with respect to the centroid of the origin polyhedron. Here they are divided into groups of quadrilaterals with the same areas for specific parameters t and q.
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.
Some useful links:
http://dmccooey.com/polyhedra/index.html Visual Polyhedra
https://www.geogebra.org/material/show/id/xtuq9vnr Uniform Models , GeoGebra, smiller2021
https://www.geogebra.org/material/show/id/SMW5dMGB Stellacje, GeoGebra, Jerzy Mil
https://www.mathconsult.ch/static/unipoly/list.html All Uniform Polyhedra
http://paulbourke.net/geometry/polyhedra/ Uniform Polyhedra (80), Compiled by Paul Bourke
Stellation
List of polyhedral stellations
List of Wenninger polyhedron models