The Pseudo-Truncated-Icosahedron

Image

Continue reading

An Icosahedron, Augmented, and Then Reaugmented, with Octahedra

Image

An Icosahedron, Augmented, and Then Reaugmented, with Octahedra

Software credit: you can try the software I used to make this at http://www.software3d.com/stella.php.

A Big Ball of Pyramids

Image

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

Image

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

Image

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.

A Variant of the Great Icosahedron

Image

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

Image

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

Image

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

Image

Cluster of 120 Dodecahedra

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

Cluster of Sixty Icosidodecahedra

Image

Cluster of Sixty Icosidodecahedra

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