Tag Archives: polyhedral

Three Stellations of the Icosidodecahedron

Image

Reply

Three Stellations of the Icosidodecahedron

The icosidodecahedron’s 24th stellation is above, and the 32nd, then the 36th, are below.

Icosidodeca 32nd StellationIcosidodeca 36th Stellation

I made these images using Stella 4d, a program you can find at www.software3d.com/Stella.php.

Odd Polyhedral Cluster

Image

Reply

Odd Polyhedral Cluster

I stumbled upon this while using Stella 4d to modify existing polyhedra. You may find this program at http://www.software3d.com/Stella.php.

A Gallery of 27 Polyhedra with Cuboctahedral Symmetry

Image

Reply

Some of these polyhedra have “normal” cuboctahedral symmetry, while others have the chiral variant of that symmetry-type — in other words, the same type of symmetry found in the snub cube.

Some Polyhedra with Cuboctahedral Symmetry

CO1Convex hullCO2 Convex hullCconvex hullDual of Convex hullhexagons and squaresStellated Convex hullStellated Convex hulllAugmented Stellated Convex hullCoonvex hullConvex hull of prism-augmented snub cubedual of Coonvex hulllreaugmented dual of Convex hull of prism-augmented snub cubeStellated Polydual of Convex hull of prism-augmented snub cubeanother augmentation of dual of Convex hull of prism-augmented snub cubedual of Coonvex hullFaceted Convex hullStellated Poly2Stellated Poly3Faceted Convex hulllStellated Poly4Dual of Convex hulglDual of Convex hugFaceted Convex hulfgdsgthxlFaceted Convex hulfgdsgthgfsxlFaceted Convex hufdlfgdsgthgfsxl

I used Stella 4d:  Polyhedron Navigator to make these images, and you can find that program at http://www.software3d.com/Stella.php.

Some Recommeded Websites for Polyhedral Enthusiasts

Posted on by
Reply

There are a lot of websites devoted to polyhedra. Here are some of the best.

This one is run by Jonathan Bowers:  http://www.polytope.net/hedrondude/home.htm.

Here’s the portal-page to George Hart’s pages, with links to a LOT of cool stuff he’s made: http://www.georgehart.com/.

I don’t know who runs this one:  http://polyhedra.org/poly/

This one is Robert Webb’s. He’s the person who wrote Stella 4d, the program I use most often on my own blog to create polyhedral images: http://www.software3d.com/Gallery.php. (Also, while we do share a first name, he is not the same person as me, as a few readers of my blog have thought in the past.)

Craig Kaplan has a page of links to other pages of his, right here: http://www.cgl.uwaterloo.ca/~csk/projects/. Of those, my favorites are the sections on John solid near-misses (http://www.cgl.uwaterloo.ca/~csk/projects/nearmisses/), as well as on symmetrohedra:  http://www.cgl.uwaterloo.ca/~csk/projects/symmetrohedra/

Jim McNeill’s polyhedra site is here:  http://www.orchidpalms.com/polyhedra/

Here’s a good one, but I don’t know its creator’s full name: http://colinspics.org/index.htm

Finally, one by Vladimir Bulatov:  http://www.bulatov.org/polyhedra/index.html

This is definitely not a complete list. If you know of other good polyhedron-oriented websites, please leave links to them in a comment on this post.

A Polyhedral Cage Which Includes the Dodecahedron, the Icosahedron, and the Rhombic Triacontahedron

Image

Reply

A Polyhedral Cage Which Includes the Dodecahedron, the Icosahedron, and the Rhombic Triacontahedron

The dodecahedron’s edges pass through the purple squares (edge midpoints) and red hexagons (vertices), and have blue decagons above their pentagonal face-centers. The blue decagons’ centers also mark the vertices of the triangular faces of the icosahedron, each of which has a purple square as a side-midpoint, and a red hexagon over its face-center. The rhombic triacontahedron’s faces have blue decagons at the vertex of each acute angle, and red hexagons at the obtuse angle vertices, with purple squares above the rhombic faces’ centers.

I used Stella 4d to make this image, and you can find that program at http://www.software3d.com/Stella.php.

A Gallery of Twenty-One Polyhedra with Icosidodecahedral Symmetry

Image

Reply

Multiple Variants of the Icosidodecahedron

Click on the smaller pictures, if you wish to enlarge them, one at a time.

convex hull of prismaugmented RTCConvex hull of prismaugmented strombic hexacontahedronConvex hull of reaugmented convex hull of augmented RTCConvex hull qConvex hull z dualConvex hull z

Those last two were duals of each other. The next two are as well.

300-faced dual of 362-faced expanded snub dodecahedron convex hull augmented with 3x prisms362-faced expanded snub dodecahedron convex hull augmented with 3x prismsDual of Convex hullID variant

These next two are duals, as are the pair that follows them.

variant on the SSDdual of variant of SSDpolyhedron xpolyhedron x dual

regularized convex hull of prism-augmented RTCtwisted Convex hullStellated rainbow thingConvex hull

I’ll finish with one more dual pair.

UnnamedUnnamed

All of these were made using Stella 4d:  Polyhedron Navigator, which is available at http://www.software3d.com/Stella.php.

Twenty Rotating Triskelions, Made of Kites

Image

Reply

Twenty Rotating Triskelions, Made of Kites

Created using Stella 4d, software available at http://www.software3d.com/Stella.php.

A Pulsating Compound of Three Octangular Dipyramids

Image

Reply

Pulsating Compound of Three Octangular Dipyramids

Software credit: see http://www.software3d.com/Stella.php for the software used (Stella 4d) to make this image. A free trial download is available.

The Compund of Three Octahedra

Image

Reply

The Compund of Three Octahedra

This polyhedral compound is part of the built-in library of polyhedra that comes with Stella 4d: Polyhedron Navigator. You can find this software here: http://www.software3d.com/Stella.php.

Three Unusual Polyhedral Compounds

Image

Reply

Three Unusual Polyhedral Compounds

The other two appear smaller here, but can be enlarged with a single click.

hybrid

All three were created using software called Stella 4d, which you may find at http://www.software3d.com/Stella.php.

strange compound