Three Views of a Rotating Cluster of 33 Icosidodecahedra

Posted on 12 November 2016 by RobertLovesPi

33-icosidodeca

To make these three rotating cluster-polyhedra, I started with one icosidodecahedron in the center, then augmented each of its 32 faces with overlapping, additional icosidodecahedra, for a total of 33 icosidodecahedra per cluster. In the first image, only two colors are used: one for the triangular faces, and another for the pentagons. The second version, however, has the colors assigned by face-type, which is determined by each face’s placement in the overall cluster.

33-icosidodeca-ft

For the third version, I simply put Stella 4d (the program I use to make these images) into “rainbow color mode.” If you’d like to give Stella 4d a try, you can do so for free at this website.

33-icosidodeca-rc

Rings of Five

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rings-of-five

Five

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five

Tessellation Featuring Regular Enneagons, Regular Hexagons, and Isosceles Triangles

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tessellation-2

Tessellation Featuring Regular Enneagons and Hexaconcave, Equilateral Dodecagons

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tessellation

A Gallery of Two Dozen Polyhedra with Icosidodecahedral Symmetry, with a Few of Them Chiral

Posted on 4 November 2016 by RobertLovesPi

12x20-20x12-30x8-120x3-182-faces-convex-hull

162-faces-12-of-them-icosagons-120-pentagons-30-rects

dual-of-convex-hull-242-faces-42-are-two-types-decagon-20-hexagons-180-pentagons

symmetrohedron-with-212-faces-including-20-octadecagons-12-pentagons-and-180-trapezoids-split-evenly-between-three-types

Any of these rotating polyhedra may be made larger with a click. I created them using Stella 4d, a program you may try (as a free trial download) at http://www.software3d.com/Stella.php.

A Gallery of Fourteen Polyhedra with Cuboctahedral Symmetry

Posted on 4 November 2016 by RobertLovesPi

Any of these rotating polyhedra may be made larger with a single click. All were created using Stella 4d, a program you may try for free at this website: http://www.software3d.com/Stella.php.

A Symmetrohedron with 74 Faces

Posted on 3 November 2016 by RobertLovesPi

74-faces-symmetroheron

Symmetrohedra have many regular faces, but irregular faces are allowed in them as well. The octagons, hexagons, and squares in this polyhedron are regular, but the 48 triangles are scalene. Here’s what it looks like with these triangles rendered invisible:

74-faces-symmetroheron-with-the-48-scalene-triagles-hidden

Stella 4d was used to make these images; it may be tried for free at this website: http://www.software3d.com/Stella.php.

My 2016 Presidential Election Prediction Map

Posted on 3 November 2016 by RobertLovesPi

election-prediction This is my predicted electoral map for Tuesday’s presidential election. If you disagree with it, you can make your own version at http://www.270towin.com.