GMTRCPLY - GeoMeTRiCPLaY

GMTRCPLY - GeoMeTRiCPLaY

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The mentioned Company and Product names are usually registered brand names and/or trademarks.
They are given for reference purposes, without any commercial intent.

This is a first attempt to define the structure. Descriptions and content will be added step by step.
For many topics, there are excellent resouces available, and I will only give a brief description.
I want to focus on the special topics and/or vintage toys.

2D Packing
Polyiamonds (triangular)
Polyiamonds are shapes made up of equilateral triangles.
Hexiamonds
A formerly widespread game is "Verhext" by Prof. Dr. Heinz Haber. The game contains twelve hexiamonds (six connected triangles each) made of red or green plastic, along with some working cards.
Polyominoes (square)
Polyominies are shapes made up of squares.
Dominoes
The Domino tiles are related to Polyominoes for being made up of two squares. There is only one way to combine two squares, therefore only one Domino exists in geometry. But how can there be so many Domino tiles, if only on Domino exists? The Domino game marks each square with a number, the unique combinations of two such numbers make up the set of Domino tiles. Usually, the sets are numbered starting with zero (blank) up to six. The dot pattern is equal to the well-known dot pattern on dice. Larger sets come in increments of three, i.e. up to 9, 12, 15 or 18. Reading the values from the dot pattern starts to get confusing above 9, so there are Domino tiles available which are marked with plain numbers. However, the dotted tiles look nicer, except maybe for the 17 and 18.
Tetrominoes
The Tetris game might even be more popular than the Domino game, these days. But only very few people know that the name is derived from the fact that the Tetris pieces are made up of four squares.
There are several real-world so-called "Tetris" games available, mostly using Tetrominoes made of painted wood.
Pentominoes

The Pentomino Game is also very popular. Most Pentomino versions use thin tiles that are used to lay out flat outlines. There are also Pentomino tiles available with a thickness of exatly one unit. They are usually called Pentomino-3D, because you can combine the Pentominoes in three dimensions in any orientation . This should not be confused with Pentacubes, where the tiles are made up of five cubies, but the cubies are combined in all directions. Pentomino-3D have an outline of n × m × 1, which means that all tiles can also be laid out flat with a height of one unit.

A widespread game is "Pentomino" by Prof. Dr. Solomon W. Golomb. The Pentominoes are made of red or green plastic. There is a large cardboard box version with working cards available, and a small plastic box version where the Pentominoes are arranged in two layers of 6×5 units.

Polyhex (hexagonal)
Polyhex are pieces made up of equilateral hexagons. There are different games available where Penta-Hexa pieces are used, i.e. pieces made up of five hexagons each. The aim is to fill up certain shapes with the tiles.
3D Packing
Soma Cube
A Soma Cube is a 3D Packing problem. The aim is to fill a 3×3×3 space using the seven Soma pieces. The base piece is an angled piece made up of trhee cubies. The other six Soma pieces are derived from the base piece by adding one cubie. The 2×2×1 piece is not used. 6 · 4 + 3 cubies will exactly fill the volume of 27 units.
Pentomino-3D

Pentomino-3D is a game where Pentomino pieces with a thickness of one unit are used. These can be arranged in three dimensions. Besides the flat combinations known from regular (flat) Pentomino pieces, certain cuboid shapes can be filled. The most popular dimensions are 6×5x2 and 3×4×5. But there are countless irregular shapes possible.

A very nice implementation of Pentomino-3D is the Travel or Pocket Katamino which uses plastic pieces with a unt size of 12mm.

Pentacubes

Pentacubes are made up of five cubies each, where the cubies can be arranged in any direction. Pentacubes contain a full set of Pentomino-3D, along with additional Pentacubes that cannot be laid flat. A full set of Pentacubes contains 29 pieces.

There is a game named "Reservat" by Ekkehard Künzell available (now distributed by Logika Spiele) that uses plastic molded Pentacubes. Wilfried Ricken uses Pentacubes made of wood for different kinds of games.

2D Assembly
Tangram
Missing Square Puzzle
3D Assembly
Loose pieces
Magnetic Pieces
Connected Pieces
Kaleidocycles
Combination, Permutation, etc.
Information: Geometric Solids
Platonic Solids
The five Platonic Solds are geometric fundamentals: Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron.
Archimedian Solids
Among the Archimedian Solids, the Truncated Icosahedron is well known as the Soccer Ball made out of pentagons and hexagons.
Catalan Solids
A real-world implementation of the Catalan Solids are multi-sided dice.
Rhombic Solids
If you are interested in Rhombic Solids: Hans Walser has many publications on the web, as PDF, and of course books.
Rhombic Dodecahedron
Rhombic Triacontahedron
Special Geometric Solids
Oloid
Gömböc
Special Relationships
Dice
Twisty Puzzles
Information: Companies, Names, Websites, Books
Gallery

The mentioned Company and Product names are usually registered brand names and/or trademarks.
They are given for reference purposes, without any commercial intent.

Hans-Jürgen Reggel   ·   http://www.hjreggel.net/gmtrcply/   ·   Imprint   ·   2021-07-13 ~ 2021-07-21