I turn 54 years old today, so here is a 54-pointed star to mark the occasion. The nine repetitions of the six colors of the spectrum work because (6)(9) = 54.
My Birthday Star for 2022
4
Tag Archives: geometry
A 38-Faced Symmetrohedron
This symmetrohedron includes, as faces, eight regular hexagons, six squares, and 24 isosceles triangles. I made it using Stella 4d, which you can try for free at this website.
The Pyritohedral Golden Icosahedron
Both the Platonic icosahedron and the golden icosahedron have twenty triangular faces. In the Platonic version, these faces are all equilateral triangles. The golden icosahedron has eight such triangles, but the other twelve are golden triangles, which have a leg-to-base ratio which is the golden ratio. These golden triangles appear in pairs, and the six pairs are arranged in such a way as to make this a solid with pyritohedral symmetry: the symmetry of a standard volleyball.
A net for the golden icosahedron appears below. Both images were made using a program called Stella 4d, which you can try for free right here.
A Faceted Rhombicosidodecahedron with 540 Faces
This beauty appeared unexpectedly when I was playing around with polyhedra related to the icosahedron and dodecahedron, using Stella 4d: Polyhedron Navigator. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.
Compound of Three “Axe Head” Polyhedra
I made this using Stella 4d, a program you can try for free right here.
A Polyhedron with 98 Faces
This polyhedron has six faces which are regular octagons, sixty quadrilateral faces, and 32 triangular faces, eight of which are regular. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
A Symmetrohedron Which Is Also a Zonohedron
I made this by zonohedrificaton of an octahedron, using its faces, edges, and vertices, and software called Stella 4d, which you can try for free right here.
This polyhedron has six regular octagons (red), a dozen octagons which are merely equilateral (yellow), eight regular hexagons, and 24 squares.
Tessellation of Regular Hexagons, Squares, and Triangles, as Well as 60/120 Degree Rhombi
Image
A Compound of Two Irregular Dodecahedra
Image
I made this using Stella 4d, software you can try for free right here.
Twelve Triangles of the Icosahedron
Icosahedra have twenty faces. In the image above, only twelve of those triangles are visible; the other eight have been hidden, so you can see what this solid looks like on the inside. The twelve which remain have pyritohedral symmetry — the symmetry of a volleyball.
I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.
RobertLovesPi.net 