The Compound of the Truncated Isocahedron and the Pentakis Dodecahedron, with Related Polyhedra

The yellow-and-red polyhedron in the compound below is the truncated icosahedron, one of the Archimedean solids. The blue figure is its dual, the pentakis dodecahedron, which is one of the Catalan solids.

Pentakis dodecahedron and truncated icosahedron

The next image shows the convex hull of this base/dual compound. Its faces are kites and rhombi.

Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Shown next is the dual of this convex hull, which features regular hexagons, regular pentagons, and isosceles triangles.

dual of Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Next, here is the compound of the last two polyhedra shown.

dual and base compound of Convex hull of trunctaed icosahedron slash pentakis dodecahedron compound

Continuing this process, here is the convex hull of the compound shown immediately above.

Convex hull

This latest convex hull has an interesting dual, which is shown below. It blends characteristics of several Archimedean solids, including the rhombicosidodecahedron, the truncated icosahedron, and the great rhombicosidodecahedron.

Dual of Convex hull

This process could be continued indefinitely — making a compound of the last two polyhedra shown, then forming its convex hull, then creating that convex hull’s dual, and so on.

All these polyhedra were made using Stella 4d: Polyhedron Navigator, which you can purchase (or try for free) at http://www.software3d.com/Stella.php

Hexagon the Kitten Is Recording My Computer Activity

So I’m looking at Facebook, and all of a sudden Hexagon the Kitten is on the keyboard. Zap! Screenshot captured at feline speed — before I could grab the little rogue.

Hexagon's schreenshot

This is the first of four pages of information which Hexagon attempted to print this morning — a screenshot of the top of my Facebook timeline. She tricked me into losing the other three pages, which were simply more records of recent activity on Facebook.

She was also, as the image above shows, trying to print in black and white, which seemed interesting. I looked it up, and cats have far more rods than cones, compared to humans, so I guess Hexagon doesn’t see color as that important.

Hexagon kitten young

She also typed the following into the keyboard:

Hexagon's typing

What is Hexagon’s goal with all of this computer activity? If I ever figure it out, I’ll post my findings here.

My Mother’s Epic Battle with an Armadillo

I just found a hilarious tale about my mother (in L. Lee Cowan’s Except for All the Snakes, I just Love It Out Here: The News from Stone County, Arkansas, Where One Life is Put Down Straight Up, p. 120). According to this published account, I was four years old when her battle to kill an armadillo entered family legend. As you can see below, Mom credits both my sister and myself with keeping the story alive over the years. A good family friend, Bruce, played a key role in bridging the gap between my mother and L. Lee Cowan, the author of the book in which this was published. It’s an amazing thing to have found.

If you like this excerpt (shown below), please buy the book, as I have done.

LLeeCohan

An Enneagonal Mandala

enneagonal mandala

I made this years ago — in 2010 — and just found it today, on Facebook. That was two years before this blog started. I like finding such “lost works,” but it doesn’t happen often these days.