Mandala Based on the Number 48

explode

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The Triangles of a Snub Dodecahedron

snub-dodeca

The snub dodecahedron, one of the Archimedean solids, has eighty faces which are triangles, and twelve pentagonal faces as well. In the view above, the pentagons are rendered invisible, allowing the interior to be viewed as the solid rotates.

The eighty triangles are of two types: the sixty yellow ones share an edge with a pentagon, and the twenty blue ones do not. If the blue triangles are also hidden, the “transparency” of this solid becomes even greater, as seen below.

snub-dodeca

Both of these images were created using Stella 4d, software you may try for free at this website.

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Three-Legged Racer

three_legged_racer

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How America Typically Sees the World

how-america-sees-the-world

This problem reaches its worst levels during presidential campaign years. It’s particularly bad during 2016.

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Building a “Polyhedral Porcupine”

This is the icosahedron, followed by its first stellation.

The first stellation of the icosahedron can be stellated again, and again, and so on. The “final stellation” of the icosahedron is the one right before the stellation-series “wraps around,” back to where it started:

icosa-stellation-final-60-spikes

This final stellation of the icosahedron would serve pretty well as a “polyhedral porcupine,” but I was seeking something even better, so I turned my attention to polyhedral compounds. This is the compound of five icosahedra:

icosahedra-5

The program I use to manipulate these solids is called Stella 4d: Polyhedron Navigator (free trial download available here). My next move, using Stella, was to create the final stellation of this five-icosahedron compound . . . and, when I saw it, I knew I had found my “polyhedral porcupine.”

icosahedra-5-final-stellation

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A Rhombic Cage

rhombic-cage

This cage is made of 36 identical rhombi, and has six openings. I made it with Stella 4d, a program available at this website.

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A Faceted Great Rhombcuboctahedron

faceted-trunc-cubocta

Some prefer to call the great rhombcuboctahedron the “truncated cuboctahedron,” instead. Whichever term you prefer, this is a faceted version of that Archimedean solid. I made it using Stella 4d: Polyhedron Navigator, software you may find here.

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