# 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

### 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)

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