# Prisms with Square-Symmetric Bases from the 29 Pentacubes

## Introduction

A *polycube* is a solid made of equal cubes joined
face to face, and a *pentacube* is a polycube with 5 cells.
There are 29 pentacubes, distinguishing mirror images:

Six pentacubes are not shown.
They are the mirror images of the chiral pentacubes,
which are shown in blue.

The letters shown in black are my names.
The green symbols are Kate Jones's names.
The red symbols are Donald Knuth's names.

Here I show four prisms with height 5,
whose bases are fully-symmetric 29-ominoes,
that can be formed by the set of 29 pentacubes.
The links in the corners show tilings by copies of a single pentacube.

A tiling for the second prism below appears at David Goodger's Polyform
Puzzler.

If you find any other such tilings by the 29 pentacubes, please write!

Last revised 2022-11-04.

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Col. George Sicherman
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