Two Non-convex Polyhedra with Cuboctahedral Symmetry

Posted on 16 January 2019 by RobertLovesPi

I made both of these while playing around with Stella 4d: Polyhedron Navigator, a program you can try out for free at http://www.software3d.com/Stella.php.

Four Symmetrohedra with Tetrahedral Symmetry

Posted on 23 November 2018 by RobertLovesPi

Symmetrohedra are polyhedra with some form of polyhedral symmetry, and many (not necessarily all) regular faces. The first two symmetrohedra here each include four regular enneagons as faces.

The next two symmetrohedra each include four regular dodecagons as faces.

All four of these were made using Stella 4d, which you can try out for free at http://www.software3d.com/Stella.php.

A Pyritohedral, Stellated Polyhedron, and Its Convex Hull

Posted on 8 July 2018 by RobertLovesPi

To make this polyhedron using Stella 4d (available here), I began with the dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, and then stellated it thirteen times.

This stellated polyhedron has pyritohedral symmetry, but this is easier to see in its convex hull:

The eight blue triangles in this convex hull are equilateral, while the twelve yellow ones are golden isosceles triangles.

A Miscellany of Polyhedra with Icosidodecahedral Symmetry

Posted on 3 December 2017 by RobertLovesPi

20 at 5 and 60 at 5 and 20 at 6 and 60 at 7 242 faces mostly quads Convex hull b starball All quads 240 faces Augmented Disdyakistriaconta Convex hull with 12 reg icosagons decagons enneagons bowtie trapezoids stellated several times Dual of Convex hullashgdfasf dual of polyhedron with 12 pentadecagons Dual of Unnamed Dual Faceted Dodeca duAL OF FIRST STELLATION OF ICOSA Faceted ICOSIDodecaHEDRAL POLYHEDRON Stellated Convex hull 2 stellated Dual of Convex hullashgdfasf Stellated Poly 4 Stellated Poly 3.gif Zonohedrified Poly.gif Unnamed Dual nc.gif Zonohedrified Icosa.gif

All of these polyhedra were made using Stella 4d: Polyhedron Navigator. If you’d like to try this program yourself, simply visit http://www.software3d.com/Stella.php, where a free trial download is available.

Some Tetrahedral Stellations of the Truncated Cube

Posted on 19 January 2017 by RobertLovesPi

a-tetrahedral-stellation-of-the-trunc-cube

another-tetrahedral-stellation-of-the-trunc-cube-2

another-tetrahedral-stellation-of-the-trunc-cube-5

another-tetrahedral-stellation-of-the-trunc-cube-3

another-tetrahedral-stellation-of-the-trunc-cube-6

another-tetrahedral-stellation-of-the-trunc-cube-4

another-tetrahedral-stellation-of-the-trunc-cube

I created these with Stella 4d, which you may try for free at this website. To make a given polyhedral stellation appear larger, simply click on it.

Tetrahedrally-Symmetric Creatures with Polyhedral Legs

Posted on 23 November 2016 by RobertLovesPi

Each of these has a tetrahedron hidden from view in the center.

augmented-tetra

augmented-tetra-2

augmented-tetra-3

augmented-tetra-4

These were made using Stella 4d, which you may try for yourself here.

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.