From octahedron to cube

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From octaedorn to cube
Octa2cube 1.jpg
On display at Museu de Matemàtiques de Catalunya
Type Hands-on, Puzzle
Topics Geometry, Polyhedra

From octaedorn to cube is a hands-on exhibit by Museu de Matemàtiques de Catalunya.


The exhibit is a puzzle of 21 wooden pieces linkable by magnets. The core piece is a black and white octahedron. Its diagonal has the same length as the edge of the cube that represents the solution of the puzzle. This octahedron is the dual polyhedron of the cube. The other pieces are 8 regular and 12 irregular tetrahedrons.

Activities and user interaction

Constructive sequence from an octahedron to a cube.

The activity proposed in the exhibition is simply to build the reproduced solids in the illustrated sequence, starting with the regular octahedron in the centre of the structure. An added difficulty is to correctly combine the pieces so that the faces of the cube always present the four colours.

It is a fairly easy activity that can play any type of public in a time appropriate to the rhythms of an exposure. The magnets hidden in the faces of the different solids make the activity quick and pleasant.

A mediator can propose some activities that allow for an "instant workshop", or altenatively for a use in the classroom. See the didactical guide (pdf).