Thirty Rhombic Pyramids Flying in Dodecahedral Formation

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Thirty Rhombic Pyramids Flying in Dodecahedral Formation

http://www.software3d.com/stella.php — That’s where you can find software to make things like this.

The Platonic Icosahedron has twenty faces which are equilateral triangles. In the Golden Icosahedron, twelve of those triangles (the yellow ones) have been replaced by acute, isosceles triangles with a leg:base ratio which is the Golden Ratio.

To try the software I used to make this, just visit http://www.software3d.com/stella.php.

Golden Rainbow Star

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Triskelion Based on the Golden Ratio

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Triskelion Based on the Golden Ratio

Incongruous Mandala

Posted on 8 February 2013 by RobertLovesPi

There’s no relationship (of which I am aware) between the Golden Ratio and regular hexagons — so of course I had to try to combine them. The results are yours to judge.

Snowflake Mandala II

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Snowflake Mandala III

The Hyperspace Analogue of the Stella Octangula

Posted on 7 February 2013 by RobertLovesPi

The simplest polyhedron is the tetrahedron, and it is self-dual. The compound of two tetrahedra puts these duals together, and is most often called the Stella Octangula, a name Johannes Kepler gave it in the early 17th Century.

In hyperspace, or 4-space, the simplest polychoron is the pentachoron, or 5-cell. Like the tetrahedron in 3-space, it is also self-dual. Here is the compound of two of them: hyperspace’s version of the Stella Octangula.

Website to find the software used to make these images: www.software3d.com/stella.php

Rhombicosidodecahedron with Invisible Squares

Posted on 7 February 2013 by RobertLovesPi

The essential facts about this Archimedean solid: it has 62 faces total (12 pentagons, 20 triangles, and 30 squares, with the squares hidden here), 120 edges, and 60 vertices.