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.

Cluster of Sixty Rhombicosadodecahedra

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