rhombic dodecahedron | RobertLovesPi.net

Long, Narrow, Multicolored Hexagons As the Edges of a Rotating, Hollow Rhombic Dodecahedron

Image

Long, Narrow, Multicolored Hexagons As the Edges of a Rotating, Hollow Rhombic Dodecahedron

Software credit: see http://www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.

Three separate programs were used to make this: Geometer’s Sketchpad, MS-Paint, and Stella 4d. The latter program was written by a friend of mine, and may be bought (or tried for free) here: www.software3d.com/stella.php.

Each of the turquoise images contains 32 circles, and each is on a face of a single rotating rhombic dodecahedron. That polyhedron, though, is obscured by having black faces against a black background, with edges and vertices not shown. You can see no more than one of an entire rhombic face at a time, and that happens only when the “lighting” provided by Stella 4d makes it appear slightly illuminated.

The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

Image

The Compound of the Rhombic Dodecahedron and Its Own Third Stellation

Software credit: see http://www.software3d.com/stella.php

A Non-Convex “Bowtie” Polyhedron

Image

To form this polyhedron, I took a rhombic dodecahedron, and augmented each of its twelve sides with additional rhombic dodecahedra, forming a cluster of thirteen of these space-filling polyhedra. I then stellated this cluster thirty-four times, and this was the unexpected result.

The software I used to do this may be found (and tried for free) at http://www.software3d.com/stella.php.

An Octahedron Partially Encasing a Rhombic Dodecahedron

Image

An Octahedron Partially Encasing a Rhombic Dodecahedron

Software credit: http://www.software3d.com/stella.php

Expanded Rhombic Dodecahedron

Image

Expanded Rhombic Dodecahedron

To make this, a rhombic dodecahedron had each of its faces augmented with prisms, and the I took the convex hull of the resulting figure. This polyhedron has fifty faces, all but eight of which are quadrilaterals.

Software credit: http://www.software3d.com/stella.php.

Rhombic Dodecahedron with Standing Waves

Image

Rhombic Dodecahedron with Standing Waves

This was created by request, using software you may try for yourself at http://www.software3d.com/stella.php.

An Intermediate Form Between the Cuboctahedron and Its Dual, the Rhombic Dodecahedron

Image

An Intermediate Form Between the Cuboctahedron and Its Dual, the Rhombic Dodecahedron

There are many ways to make intermediate forms between dual polyhedra. This was made using the expansion method. The faces of the cuboctahedron (red and blue) were moved outward, as were the green faces of the rhombic dodecahedron, until the meeting of all possible vertices. The yellow rectangles were the spaces created between faces by this expansion.

(Software credit: see http://www.software3d.com/stella.php)