Pentacubes: Puzzles & Solutions

Author: David Goodger <>
Date: 2015-02-24
Revision: 600
Web site:
Copyright: © 1998-2015 by David J. Goodger
License:GPL 2


The pentacubes are named as per the pentominoes (planar), with the non-planar pentacubes following Kadon's "Superquints" naming. High-quality hardwood sets of pentacubes are available from Kadon Enterprises as Super Deluxe Quintillions (equivalent to the Pentacubes Plus pieces below). Add the Poly-4 Supplement to get all polycubes of order 1 through 4 as well (see Polycubes: Puzzles & Solutions).


The 29 pentacubes cannot form a simple box-shaped solid. Other forms are possible however:

Open Boxes

(closed on the bottom)


3x9x9 Open Box: solutions incomplete (X3D model)


18x3x3 Open Box (design from Kadon's Super Quintillions booklet): solutions incomplete (X3D model)


2x7x15 Open Box: solutions incomplete (X3D model)

Highrise Towers


3x3x20 Tower 1 (design by Nick Maeder): solutions incomplete (X3D model)


3x3x20 Tower 2 (design by Nick Maeder): solutions incomplete (X3D model)


3x3x19 Crystal Tower: solutions incomplete (X3D model)


Pentacubes Plus

Sold under the name "Super Deluxe Quintillions" by Kadon, these 30 pieces are the 29 pentacubes plus a second L3 piece (a.k.a. J3), allowing the construction of box shapes.

Non-Convex Pentacubes

There are 28 non-convex pentacubes: all of the pieces that have at least one inside corner. These are just the 29 regular pentacubes less the "I" (straight) pentacube, the only convex piece. The advantage of this set is that, like the Pentacubes Plus set, box shapes can be formed. Also, lacking the 5-cube-long "I" pentacube, more convoluted shapes can be formed.


Dorian Cubes

These puzzles are constructed from the 25 pentacubes that each fit within a 3×3×3 box (omitting the I, L, N, and Y pentacubes).

Designed by Joseph Dorrie. Referenced on p. 41 of Knotted Doughnuts and Other Mathematical Entertainments, by Martin Garder, 1986.