Sources page biographical material

6.AZ. BALL PYRAMID PUZZLES
This section is largely based on Gordon's Notes, cf below. See also 6.AP.2 for dissections of a tetrahedron in general. This section is now expanding to consider all polysphere puzzles.

See also S&B, p. 42, which mentions Hein and some other versions.

Piet Hein. Pyramystery. Made by Skjøde of Skjern, Denmark, 1970. With leaflet saying it was "recently invented by Piet Hein.... Responding to numerous requests, the inventor has therefore obliged the many admirers of the puzzle by also inventing its history". He then gives a story about Cheops. Peter Hajek and Jerry Slocum have different examples!!

Hajek's example has four planar rectangular pieces: 1 x 4, 2 x 3, 3 x 2, 4 x 1 rectangles. It is the same as Tut's Tomb -- see below. It has a 4pp English leaflet marked © Copyright Piet Hein 1970.

Slocum's example has 6 planar pieces: 4 3-spheres and 2 4-spheres. The leaflet is 34pp (?? -- Slocum only sent me part of it) with 3pp of instructions in each of 9 languages and then 6pp of diagrams of planar and 3-D problems. It is marked © 1970 Aspila, so perhaps this is a later development from the above?? The story part of the text is very similar to the above, but slightly longer. The pieces make an order 4 tetrahedron or two order 3 tetrahedra or two order 4 triangles and one can also divide them into two groups of three pieces such that one group makes an order 3 tetrahedron, but the other does not.

Advertising leaflet for Pyramystery from Piet Hein International Information Center, ©1976, describes the puzzle as having six pieces.

Mag Nif Inc. Tut's Tomb. c1972. Same as the first Pyramystery.

Akira Kuwagaki & Sadao Takenaka. US Patent 3,837,652 -- Solid Puzzle. Filed: 1 May 1973; patented: 24 Sep 1974. 2pp + 4pp diagrams. Four planar 3-spheres and a 2-sphere to make a square pyramid of edge 3. 11 planar 4-spheres to make an octahedron shape of edge 4. Cites a 1936 Danish patent -- Hein ??NYS

Len Gordon. Perplexing Pyramid. 1974. Makes a edge 4 tetrahedron with 6 planar right-angled pieces: domino; straight and L trominoes; I, L, Y tetrominoes.

Patrick A. Roberts. US Patent 3,945,645 -- Tangential Spheres Geometric Puzzle. Filed: 28 Jun 1976; patented: 29 Nov 1977. 3pp + 3pp diagrams. 8 4-spheres and a 3-sphere to make a tetrahedron of side 5. 5 of the 4-spheres are non-planar.

Robert E. Kobres. US Patent 4,060,247 -- Geometric Puzzle. Filed: 28 Jun 1976; patented: 29 Nov 1977. 1p + 2pp diagrams. 5 pieces which make a 4 x 5 rhomboid or a tetrahedron. Two pieces have the form of a 2 x 3 rhombus; two pieces are 2-spheres and the last piece is the linear 4-sphere.

Len Gordon. Some Notes of Ball Pyramid and Related Puzzles. Revised version, 10 Jul 1986, 14pp. Available from the author, 2737 N. Nordic Lane, Tucson, Arizona, 85716, USA.

Ming S. Cheng. US Patent 4,988,103 -- Geometric Puzzle of Spheres. Filed: 2 Oct 1989; patented: 29 Jan 1991. Front page, 5pp diagrams, 4pp text. A short version is given in Wiezorke, 1996, p. 64. 7 planar 5 spheres to make a tetrahedron; a hexagon with sides 3, 4, 4, 3, 4, 4; an equilateral triangle lacking one vertex.

Bernhard Wiezorke. Puzzling with Polyspheres. Published by the author (Lantzallee 18, D 4000 Düsseldorf 30, Germany), Mar 1990, 10pp.

Bernhard Wiezorke. Compendium of Polysphere Puzzles. (1995); Second Preliminary Edition, as above, Aug, 1996. 64pp, reproducing the short versions of the above patents. Despite Wiezorke's searches, nothing earlier than Hein's 1970 puzzles has come to light.

Torsten Sillke & Bernhard Wiezorke. Stacking identical polyspheres. Part 1: Tetrahedra. CFF 35 (Dec 1994) 11-17. Studies packing of tetrahedra with identical polysphere pieces, with complete results for tetrahedra of edges 4 - 8 and polyspheres of 3, 4, 5 spheres. Some of the impossibility results have only been done by computer, but others have been verified by a proof.