A Big Ball of Pyramids

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A Big Ball of Pyramids

To create this, a central rhombicosidodecahedron had each of its faces augmented by pyramids, each of which uses only equilateral triangles for lateral faces.

Software credit: The program used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.

A Polyhedron Featuring 152 Faces

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A Polyhedron with 152 Faces

The 152 faces of this polyhedron are:

    • 12 regular pentagons
    • 60 trapezoids
    • 20 small, equilateral triangles
    • 60 large, slightly-isosceles triangles

This software used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.

A Breathing Cube

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A Breathing Cube

This software used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php. The “breathing” effect is optional with this program, and is created by having the software use a tight fit-to-frame in each still pic that composes this .gif file.

Your Toes Are Younger Than Your Head

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Your Toes Are Younger Than Your Head

Unless, like a bat, you sleep upside-down, your toes are younger than your head.

Why?

Because, having spent more time slightly closer to the center of the earth, they have endured a slightly stronger gravitational field strength. This, in turn, due to relativistic time dilation, slows time down for your toes, relative to your head. With a slower passage of time during all periods when you were upright, less time has passed for them — and so they are younger.

Image credit: http://www.bestpodiatristnyc.com/british-hammertoes-are-wonky-toes/#sthash.xKDfxbgJ.dpbs

A Polyhedral Snowman

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A Polyhedral Snowman

We’re out of school today because of an ice storm, and I wanted to make a snowman. However, we got very little snow — mostly freezing rain and sleet fell — so I can’t make a traditional snowman. Also, it’s really cold outside. So, instead, I stayed inside, where it’s warm, and made a polyhedral snowman out of (from top to bottom) an icosahedron, an icosidodecahedron, and a rhombicosidodecahedron.

Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software used to make this image.

A Variant of the Great Icosahedron

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Faceted Dual

The great icosahedron has 20 faces which are interpenetrating equilateral triangles, most of which are hidden in the interior of that polyhedron. The non-hidden, and therefore visible, parts are called “facelets” — and there are 180 of them: 120 scalene, and 60 isosceles.

In this variant of the great icosahedron, the sixty isosceles facelets are simply missing, which changes the shape of the remaining 120, still-scalene facelets. The color scheme is one which gives each facelet a different color — except for coplanar or parallel facelets, which are the same color, making them easier to spot.

Software credit: see http://www.software3d.com/stella.php — with a free trial download available there.

A Stellated Polyhedron

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A Stellated Polyhedron

Software credit: see http://www.software3d.com/stella.php — free trial download available.

What exactly did I stellate to get this polyehdron? Well, it took a long time, was based on polyhedra previously posted tonight, and was complicated. To retrace my steps, and find the exact “recipe” for this polyhedron, would require work I am simply not in the mood to do.

I like it, and am therefore blogging it, for purely aesthetic reasons.

The Twelve Five-Valent Vertices of a Rhombic Triacontahedron, Peeking Through Each Face of a Dodecahedron

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The Five-Valent Vertices of a Rhombic Triacontahedron, Peeking Through Each Face of a Dodecahedron

Software credit: see http://www.software3d.com/stella.php — free trial download available.

Cluster of 120 Dodecahedra

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Cluster of 120 Dodecahedra

Software credit: see http://www.software3d.com/Stella.php — free trial download available.

Cluster of Sixty Icosidodecahedra

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Cluster of Sixty Icosidodecahedra

Software credit: see http://www.software3d.com/stella.php — free trial download available.