- Tiling Problems and News - open problems and new solutions
- LEX notation scheme for polycubes. This can be used for polyspheres too.

Ekkehard Künzell wrote a book (in German) on games played with pentacubes.
There he explains his pentacube numbering system.
The book is sold by Ingo Uhl GmbH in Germany.
Look after the *reservat book*.
There is another human-friendly
pentacube naming system
from Kate Jones of Kadon Enterprises, Inc..
She made also a
hexomino naming system.

Here is my new systematic numbering scheme for polycubes. It is the lexicographic numbering of the coordinates. Mirror images a noted by negative numbers.

- 10 - I-Pentomino (only the pentacube itself)
- 11 - L-Pentomino List complete
- 12 - Y-Pentomino List complete
- 13 - V-Pentomino List complete (3D)
- 20 - Z-Pentomino (found by Wolf in 1997)
- 21 - 21-Pentacube List incomplete
- 30 - W-Pentomino List incomplete
- 31 - 31-Pentacube List complete
- 33 - 33-Pentacube (5x8x8 by H. Postl)
- 35 - 35-Pentacube List (not boxable)
- 37 - 37-Pentacube (7x8x20 by H. Postl)
- 40 - N-Pentomino List complete (3D) by H. Postl
- 41 - 41-Pentacube List complete
- 50 - X-Pentomino (not boxable)
- 51 - 51-Pentacube (7x8x20 by H. Postl)
- 60 - P-Pentomino List complete
- 61 - 61-Pentacube List complete
- 70 - F-Pentomino List complete (3D)
- 71 - 71-Pentacube List complete
- 80 - T-Pentomino List incomplete
- 81 - 81-Pentacube List complete (3D)
- 82 - 82-Pentacube List incomplete
- 90 - U-Pentomino List complete

- Q5 - Pseudo-Pentomino List complete (3D) by H. Postl
- J5 - Pseudo-Pentomino List incomplete
- glider - Pseudo-Pentomino List complete (2+3D) by H. Postl
- large-u - Pseudo-Pentomino List incomplete
- o o . o . o o - tiling of the plane

- Handed Pentominoes - solution by Mike Reid
- Handed Y5 rectangles - solution by Yuri Aksyonov

- Cube 5 - Cubes with like Pentacubes.
- Cube 6 - Cubes with like Hexacubes.
- 5 cube with T4 - packing with one hole
- Tricubes - tiling the 3-cube.
- Trisect the cubes - tiling the 3-cube.

- 3-Cube Puzzles - Johan Myrberger's list of 3x3x3 cube puzzles
- 4 Cube - the 12 asymmetric pentacubes plus a tetracube
- SOMA cube secrets - restrictions you should know
- REHM's cubes - other 3-cubes with different tricubes and tetracubes
- Rubik's Mini Bricks - edge-connected tricubes
- Dorian Cube - 5-cube made of pentacube fitting into a 3-cube (german)
- 7 polycubes - 3-cube with unique solution
- Egg Box - a cube of Wolfgang Schneider

- Prime Box List of Tetras - Tetracube Lists and Proofs (german)
- Prime Box List of J4 - Pseudo-Tetromino List complete (3D) by H. Postl

- p7 - p-Heptomino List complete
- p7.2 - p2-Heptomino List complete (3D)
- p7.3 - p3-Heptomino List complete (3D) (the nost interesting one)

- Restricted L3 rectangles - a word problem
- Squares with the Baumeister Set - Soma set plus I3
- squares with a hole - n*n = (n+1)(n-1) + 1
- N5 tilings - rectangles without corners
- Symmetric Packings - with an odd number of polyominoes
- Antislide - with dominoes
- Squaring the Square - without common factors
- Subblock free - tilings
- 3 layer L3 - smallest nontrivial packing
- unfold - the cube and hypercube
- Tiling the plane - 3 problems of Glenn C. Rhoads
- Cubic Pentomino Fence - solution to the fence problem

- Notation - polyshperes up to 5 spheres
- 3-Bone Impossibles - impossible tetrahedra
- A Trisphere Triangle - a word problem
- Packing Tetrahedra with Polyspheres of the same kind - For several polyspheres all possible tetrahedra have been determined. All polyspheres upto n=8 and tetrahedra (length upto 8) have been computed. Part of this work has been published in CFF. List of Polysphere Packings in german.
- The Impossible Tetrahex Triangle - the impossibility of a simple proof
- The Giant Pyramid - Gordon
- Tetrahedra of 4-9 - list complete
- Convex hexagons of 4-9 - list of figures
- Tetrahedra of 5-64 - list complete

- 25 Triangles - The Triangle of Dirk Hanneforth
- Soccer Ball matching - A puzzle with 20 hexagons and 12 pentagons
- Triangle tiling (4 colors) - An impossible symmetric tiling problem (in german)
- Drei 3*3 Legespiele - Three 3*3 Matching Puzzles (Postscript, german)

- Dancing Links (ps-file) - Knuths fast backtrack method
- Arrange - a tiling program of Udo Sprute.

- Polyomino Tilings - Micheal Reid's packings of like Polyomonoes
- Polyform Tilings - Andrew Clarke's wonderful site with good graphic and information
- Polyominoes - Kevin's Polyominoes Home Page (program, counting polyominoes)
- The Pentominoes Pages - of Jay Jenicek
- The Puzzling World of Polyhedral Dissections - Stewart T. Coffin (online version)
- SOMA Cube - Thorleif's SOMA page, a must for the soma fan
- Erich's Packing Center - Erich Friedman's is packing squares, circles, ... (with animations)
- The Geometry Junkyard - mathematical oriented stuff by David Eppstein.
- Polyforms - Miroslav Vicher's Puzzles Pages
- Polyforms - Theo Steine's polyform puzzles
- Burr Puzzles - a comprehensive burr puzzle site.
- heptomino boxes and solution set of heptomino boxes - The 108 heptominoes (with unit thickness) packed into boxes.
- Kadon Enterprises - you look for a set of pentominoes, pentacubes, ... ?
- convex tiling pentagons - It lists all 14 basic types of convex tiling pentagons.

- Tetracubes - Problems for Tetracubes without the blocks (Update)

- Pentacube contest - yearly
- Pentacube figures - some problems of mine
- Pentacube Contest 90 - a solution (with german notes)
- Pentacube Contest 91 - a solution (with german notes)
- Pentacube Contest 92 - a solution (with german notes)
- Pentacube Contest 93 - a solution (with german notes)
- Pentacube Contest 93a - a solution (with german notes)
- Pentacube Contest 94 - a solution (with german notes)
- Pentacube Contest 95 - a solution (with german notes)
- Pentacube Contest 96 - a solution (with german notes)
- Pentacube Contest 97 - a solution (with german notes)
- Pentacube Contest 98 - a solution (with notes)
- Pentacube Contest 99 - a solution (with notes)
- cff contest 35 solution - the tub problem
- cff contest 36 solution - a pentacube panorama
- Truncated Tetrahedra - a high symmetric pentacube problem of Micheal Reid

- SOMA cube secrets - restrictions you should know
- REHM's cubes - other 3-cubes with different tricubes and tetracubes
- Handed Y5 rectangles - solution by Yuri Aksyonov
- 5 Boxes 5x2x2 - an impossible pentacube problem
- 5 Cubes 3x3x3 - an impossible pentacube problem
- 3-Bone Impossibles - impossible tetrahedra
- List of Polysphere Packings in german.
- The Impossible Tetrahex Triangle - the impossibility of a simple proof
- restricted packings - polycubes which have modular restrictions
- Prime Box List of Tetras - Tetracube Lists and Proofs (german)
- Antislide - with dominoes

- A Trisphere Triangle - a word problem
- Handed Pentominoes - solution by Mike Reid
- Polynomials and Polyominoes - ideal technique by Kelly
- Filling Boxes with Bricks - by de Bruijn
- free Group technique - Famin (quantum)

Torsten Sillke, Home | FSP Mathematisierung | Fakultät für Mathematik | Universität Bielefeld

last changed 2009-01-04