a pyramid full of resources

starting pyramid


"pod" of three pyramids

This modest regular pyramid, six of whom build a cube, allows other nice assemblages.

six bipyramids
build a rhombic dodecahedron

twelve bipyramids
build a stellated rhombic dodecahedron

and with eight more "pods"
we get a cube (made up of 48 pyramids)

the Yoshimoto cube-star

And more! Let us take an Yoshimoto cube and replace the eight elementary cubes with eight "pods" (assembled with the same eight hinges). We get an orthomorph made up of 24 pyramids which takes, during its cycle, two outstanding positions: a hollow cube and a stellated rhombic dodecahedron which fills exactly the cavity of the cube! The puzzle build with two of these objects is also known as the "Shinsei Mystery".

Yoshimoto cube

This object has probably been discovered independently by several researchers but it is attributed to the Japanese designer Naoki Yoshimoto (1971) who build a great model made of gold and silver (Museum of Modern Art in New York). Copies are sold at the MoMA store.

Be patient during the initialization!

Here is a video from Philip Brocoum (1:15 - 4.6 Mb) which shows how to handle the complete object (you can continue your visit during the loading which may be long with a slow connection).

references: •  Metamorphs  by Robert Byrnes (Tarquin - 2004), with 14 nets
•  the Shinsei Mystery (in German)

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convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects September 2004
updated 30-11-2009