How can I create a snub rhombicuboctahedron using Stella4D? This polyhedron has 74 faces, 120 edges, and 48 vertices.
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snub rhombicuboctahedron
snub rhombicuboctahedron
I was able to tinker my way to a solution fortunately.
1. Begin with a rhombicuboctahedron.
2. Zonohedrify this by creating a true zonohedron. Add zones based on all faces. This produces a truncated rhombicuboctahedron.
3. Switch to faceting mode. A snub rhombicuboctahedron can be created as a faceting of the truncated rhombicuboctahedron. The equilateral triangular and square faces of the snub rhombicuboctahedron share vertices with the hexagonal and regular octagonal faces of the truncated rhombicuboctahedron, and the parallelogrammatic faces vertices with the elongated octagonal faces. Complete the remaining faceting preview by selecting vertices to create two scalene triangles (their shortest sides share an edge).
4. Create the faceted polyhedron.
5. Try to make the faces regular.
You now have a snub rhombicuboctahedron!
1. Begin with a rhombicuboctahedron.
2. Zonohedrify this by creating a true zonohedron. Add zones based on all faces. This produces a truncated rhombicuboctahedron.
3. Switch to faceting mode. A snub rhombicuboctahedron can be created as a faceting of the truncated rhombicuboctahedron. The equilateral triangular and square faces of the snub rhombicuboctahedron share vertices with the hexagonal and regular octagonal faces of the truncated rhombicuboctahedron, and the parallelogrammatic faces vertices with the elongated octagonal faces. Complete the remaining faceting preview by selecting vertices to create two scalene triangles (their shortest sides share an edge).
4. Create the faceted polyhedron.
5. Try to make the faces regular.
You now have a snub rhombicuboctahedron!
snub rhombicuboctahedron
Thanks, Ulrich!
There is another way to create those models easily: You take the cuboctahedron and hit the "Morph duals by Expansion"-button All edges are replaced by quadrilaterals. You put the result into a Memory, retrieve it and activate the base model view again. Then you facet the squares, triangles and rhombs in their original shape by hitting ctrl + right click. The remaining tetragons are faceted to two coplanar triangles each. Faceting is complete now and after creating the new polyhedron and making the faces regular you got it.
This works with the icosidodecahedron, the truncated tetrahedron, trunc octahedron, trunc cube, trunc dodecahedron and the trunc icosahedron too (in combination with the "Project onto sphere"-tool).
Ulrich
This works with the icosidodecahedron, the truncated tetrahedron, trunc octahedron, trunc cube, trunc dodecahedron and the trunc icosahedron too (in combination with the "Project onto sphere"-tool).
Ulrich