A Compound of an Octahedron and a Pyritohedral Dodecahedron

Posted on 28 May 2018 by RobertLovesPi

compound of a pyritohedral dodecahedron and an octahedron

I made this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

An Offspring of a Dodecahedron and a Tetrahedron

Posted on 26 May 2018 by RobertLovesPi

Dodeca tetrahedrally stellated mutliple times

Stellated Dodeca.gif

Stellated Dodeca rb

To make this polyhedron, I first changed the symmetry-type of a dodecahedron from icosahedral to tetrahedral, then stellated it twice. This was done using Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.

Creating a New Polyhedron from the Snub Dodecahedron

Posted on 13 September 2017 by RobertLovesPi

Shown below are the snub dodecahedron and its dual, the pentagonal hexecontahedron.

Seeking a way to make a “new” polyhedron (one never seen before), I augmented each face of the orange dual, above, with prisms. These prisms have a height equal to twice the average edge length of their bases.

Augmented Penta Hexeconta

Next, I used the software I use to manipulate polyhedra (Stella 4d, available here) to create the convex hull of this augmented pentagonal hexecontahedron.

starball before ttmfr expanded pentagonal hexacontahedron

Finally, I used Stella’s “try to make faces regular” function, and obtained this result, which I liked enough to stop here. There’s no way for me to know with certainty that this polyhedron has never been seen before, of course, but that didn’t stop me from having fun making it.

Unnamed starball.gif

Selected Stellations of the Truncated Dodecahedron

Posted on 17 July 2017 by RobertLovesPi

This is the truncated dodecahedron. It is one of the Archimedean solids.

Trunc Dodeca

This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation.

16th stellation of Trunc Dodeca

Here is the 21st stellation.

21st stellation of Trunc Dodeca

It’s easy to stellate polyhedra rapidly, and make many other changes to them, with Stella 4d: Polyhedron Navigator. You can try it for free at http://www.software3d.com/Stella.php.

25th stellation of Trunc Dodeca.gif

The stellation shown immediately above is the 25th, and the one shown immediately below is the 27th.

27th stellation of Trunc Dodeca

Here is the next stellation: the 28th. Unlike the ones shown above, it is chiral.

28th stellation of Trunc Dodeca.gif

This is the truncated dodecahedron’s 31st stellation.

31st stellation of Trunc Dodeca.gif

This one is the 38th stellation.

38th stellation of Trunc Dodeca.gif

This one is the 44th.

44th stellation of Trunc Dodeca.gif

The last one shown here is called the truncated dodecahedron’s final stellation because, if it is stellated once more, it returns to the original truncated dodecahedron.

Final stellation of Trunc Dodeca

A Rhombic Dodecahedron, Made of Icosahedra, and Tall Triangular Antiprisms

Posted on 10 June 2017 by RobertLovesPi

Augmented Icosa

Software used: Stella 4d, available at http://www.software3d.com/Stella.php.

Op Art on a Dodecahedron

Posted on 17 April 2017 by RobertLovesPi

Dodeca

I used Geometer’s Sketchpad and MS-Paint to make the designs on the faces, and then assembled the dodecahedron with Stella 4d, a program you may try here.

A Dozen Pulsating Dodecahedra

Posted on 6 April 2017 by RobertLovesPi

12 dodecahedra

To make this using Stella 4d (available here) I started with an icosahedron, placed a dodecahedron on each of its vertices, then rendered the central icosahedron invisible. The slight pulsating effect is caused by the program fitting the polyhedra tightly into each frame of the animation.

The Dodecahedron, Made from Smaller Polyhedra

Posted on 14 November 2016 by RobertLovesPi

augmented-rhombic-triaconta-dodeca

The polyhedra at the vertices are rhombic triacontahedra, and the yellow edges are elongated rhombic prisms. This was made using Stella 4d, software you may try for free at this website.

Four Sets of Five Circles On Each of the Faces of a Dodecahedron

Posted on 25 April 2016 by RobertLovesPi

Dodecahedron

After using Geometer’s Sketchpad and MS-Paint to make the image on the faces (seen alone in the last post), I then used Stella 4d: Polyhedron Navigator to project these images onto a red dodecahedron, and create this .gif. Stella is available, including as a free trial download, at http://www.software3d.com/Stella.php.

A Hybrid of the Tetrahedron and the Great Dodecahedron

Posted on 18 January 2016 by RobertLovesPi

I made this by stellating a dodecahedron repeatedly, but doing so with Stella 4d, the polyhedral-manipulation software I use (available here), set to use tetrahedral symmetry, rather than the higher-order icosahedral symmetry (which I often call “icosidodecahedral” symmetry) inherent to Platonic dodecahedra.

Hybrid of great Dodeca and the tet