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 nine 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.

Tilings for the first two prisms below appear at David Goodger's Polyform Puzzler.

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

See also

  • Full Symmetry with the 29 Pentacubes
  • Pentacube Odd Cakes
  • I L P
    I J L P Y
    I J L P U
    I P
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    Last revised 2026-10-01.


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    Col. George Sicherman [ HOME | MAIL ]