Tessellation Featuring Regular Enneagons, Regular Hexagons, and Isosceles Triangles

Tessellation Featuring Regular Enneagons and Hexaconcave, Equilateral Dodecagons

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.

A Zonohedron with 1382 Faces

Posted on 1 November 2016 by RobertLovesPi

zonohedrified-stellated-icosa

I used Stella 4d to make this zonohedron. This program may be tried for free at http://www.software3d.com/Stella.php.

An Open Cluster of Polyhedra

Posted on 29 October 2016 by RobertLovesPi

augmented-icosa

From the center to the outside, this cluster contains one icosahedron, twenty octahedra, twenty icosidodecahedra, twenty more octahedra, and, finally, twenty rhombicosidodecahedra.

augmented-icosa-dc

All three of the images here were created using Stella 4d, a program you may try, free, at this website.

augmented-icosa-rc

A Festive Cluster of Polyhedra

Posted on 26 October 2016 by RobertLovesPi

augmented-icosa-with-tet-then-octahedra

This is what you get if you start with an icosahedron, augment each of its faces with tetrahedra, and then augment the tetrahedral faces with octahedra. I made it using Stella 4d, a program you may try for free at http://www.software3d.com/Stella.php.

Two Dozen Kites Each, in Three Sets, as Faces of a Polyhedron

Posted on 22 October 2016 by RobertLovesPi

3-sets-of-two-dozen-kites-per-type

This was created using Stella 4d, a program you can buy, or try for free, at http://www.software3d.com/Stella.php.

Icosahedral Cluster

Posted on 20 October 2016 by RobertLovesPi

augmented-great-icosa

The great icosahedron, one of the Kepler-Poinsot solids, is hidden from view at the center of this cluster. Each of its faces is augmented with a Platonic icosahedron, producing what you see here. Stella 4d is the software I used; more information about that program may be found here.