Pentacubits – the puzzle pieces

Pentacubits – a puzzle based on a rhombus

Each of the 12 Pentacubits consists of 5 rhombi. Pentacubits belong to the family of Polycubits.

The basic shape of a Polycubit is a rhombus with two 60° and two 120° interior angles. These rhombi fit seamlessly into the Cubit grid shown.

The number of distinct shapes is 1 for Dicubits, 3 for Tricubits, 4 for Tetracubits, 12 for Pentacubits, 27 for Hexacubits, and 78 for Heptacubits.

12 Pentacubits on the Cubit grid
12 Pentacubits on the Cubit grid

Pentacubits puzzles

Symmetrical shapes made from Pentacubits

The 12 Pentacubits consist of 60 rhombi in total. The 3D-printed puzzle has an approximately equilateral triangular shape made up of 63 rhombi. One Tricubit was therefore added.

The underlying Cubit grid allows shapes with six axes of reflection and sixfold rotational symmetry. However, fully symmetrical shapes made exclusively from the 12 Pentacubits are probably impossible.

Fully symmetrical shape made from Pentacubits and one Tricubit
Fully symmetrical shape made from Pentacubits and one Tricubit

Some shapes made from Pentacubits

Pentacubits shape 1
Solution to Pentacubits shape 1
Pentacubits shape 2
Solution to Pentacubits shape 2
Pentacubits shape 3
Solution to Pentacubits shape 3
Pentacubits shape 4
Solution to Pentacubits shape 4
Pentacubits shape 5
Solution to Pentacubits shape 5
Pentacubits shape 6
Solution to Pentacubits shape 6

Resources & Downloads

3D-Printing Templates

The 3D-printing files include the 12 Pentacubits, one Tricubit, and a box.

3D-printed Pentacubits puzzle
3D-printed Pentacubits pieces