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Two Polyhedral Compounds

 

 

Compound of the RTC and a strombic hexacontahedron

The image above is a compound of the rhombic triacontahedron (the dual of the icosidodecahedron) and a strombic hexacontahedron (the dual of the rhombicosidodecahedron). Below, you’ll find a compound of twelve square-based pyramids, all with their “centers of mass” (assuming uniform density) displaced, from the compound’s center, by equal amounts. In response to a request I have…

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A Polyhedral Shuttlecraft, Adrift in Outer Space

Most of the polyhedra I post here have one of the symmetry-types which are collectively called “polyhedral” symmetry: tetrahedral, cuboctahedral, icosidodecahedral, or chiral variants of these.

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A Polyhedral Boomerang, in Flight

Most of the polyhedra I post here have one of the symmetry-types which are collectively called “polyhedral” symmetry: tetrahedral, cuboctahedral, icosidodecahedral, or chiral variants of these.

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A Collection of Polyhedra with Cuboctahedral Symmetry

A Collection of Polyhedra with Cuboctahedral Symmetry

I have received a request to slow down the rotational speed of the polyhedral models I make and post here, and am going to try to do exactly that. First, though, I need to empty my collection of already-made image files which haven’t yet been posted, so that I can start again, with models which rotate more slowly, after deleting all the “speedy” ones. From my backlog of polyhedral images to post,…

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A Collection of Rotating Polyhedra with Icosidodecahedral Symmetry

I’ve received a request to slow down the rotational speed of the polyhedral models I make and post here, and am going to try to do exactly that. First, though, I need to empty my collection of already-made image files which haven’t yet been posted, so that I can start again, with models which rotate more slowly, after deleting all the “speedy” ones. From my backlog of polyhedral images to post,…

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An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual

An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual

Icosahedron Augmented with Triangular Cupolae

After making the above polyhedron using Stella 4d (a program you can try for free at www.software3d.com/Stella.php), I checked its dual, which is shown below. I was surprised at its appearance, for it resembles a stellated polyhedron, even though it was created by a completely different process.

Icosahedron Augmented with Triangular Cupolae's Dual

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A Pentagonal Dokaiheptacontaheron

The 72 faces of this polyhedron are all pentagons. Twelve are regular, while the other sixty are not.

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How to Distinguish Between the Waxing and Waning Moon, At a Glance

How to Distinguish Between the Waxing and Waning Moon, At a Glance

DC

This is a waxing moon, meaning the sunlit portion we can see is growing. The outer curve also makes this view of the moon shaped more like the letter “D,” compared to the letter “C.” For the useful mnemonic here, remember that “D” stands for “developing.” D-shaped moons are in the waxing part of their cycle of phases, growing larger for about two weeks.

DGLater in the waxing portion of the moon’s…

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Three Different Stellations of the Rhombic Triacontahedron

Three Different Stellations of the Rhombic Triacontahedron

Rhombic Triaconta stellation

These polyhedra are selected from the the (long) stellation-series of the rhombic triacontahedron. Stellating polyhedra, and manipulating them in other ways, is easy with Stella 4d, which you can try as a free trial download here:   www.software3d.com/Stella.php.

stellated RTC one of many

stellated RTC another of many

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