animated cubic puzzles

three identical pyramids build a cube
this square pyramid with edges √1, √2 and √3 obviously fills the space

four regular pyramids and a regular tetrahedron build a cube

see also the decomposition of the cube into six Schläflis' birectangular tetrahedra

cubes which transform themselves into dodecahedra

rhombic dodecahedron: cube augmented with six pyramids
the six pyramids fill exactly the cube
(the ratio of the volumes is exactly 2)
regular dodecahedron: cube augmented with six "roofs"
the hole in the cube is a curious dodecahedron
(the ratio of the volumes is about 1.927)
These two objets are not very difficult to carry out. Here are technical data useful to build them:
edges: cube  1   -   dodecahedron  ½√3 ≈ 0,866
height pyramid:  ½
net: 6 squares with side  1
24 isosceles triangles  ½√3-1-½√3
edges: cube  φ = golden ratio ≈ 1,618   -   dodecahedron  1
height "roof":  ½   -   length "ridgepole": 1
net: 6 squares with side  φ
12 golden triangles  1-φ-1
12 "golden" trapeziums  φ-1-1-1

a bipyramid to build a cube or a rhombic dodecahedron

Four of these bipyramids build a cube, and eight a rhombic dodecahedron.
Of course this hexahedron fills the space.

Be patient during the initialization! (reload the page if an animation doesn't start)

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convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects February 2000
updated 18-01-2009