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Twisted geometries are discrete geometries that play a role in loop quantum gravity and spin foam models, where they appear in the semiclassical limit of spin networks. [1] [2] [3] A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph. [4]
A Tuttminx (/ ˈ t ʊ t m ɪ ŋ k s / or / ˈ t ʌ t m ɪ ŋ k s /) is a Rubik's Cube-like twisty puzzle, in the shape of a truncated icosahedron. It was invented by Lee Tutt in 2005. [1] It has a total of 150 movable pieces to rearrange, compared to 20 movable pieces of the Rubik's Cube.
During the Rubik's Cube craze of the 1980s, at least two twisty puzzles sold had the form of a rhombicuboctahedron (the mechanism was similar to that of a Rubik's Cube) [20] [21] Another example may be found in dice from Corfe Castle, each of whose square faces have marks of pairs of letters and pips. [22] The rhombicuboctahedron may also ...
Many such puzzles are mechanical puzzles of polyhedral shape, consisting of multiple layers of pieces along each axis which can rotate independently of each other. Collectively known as twisty puzzles, the archetype of this kind of puzzle is the Rubik's Cube. Each rotating side is usually marked with different colours, intended to be scrambled ...
If you expand an icosidodecahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and patch the square holes in the result, you get a rhombicosidodecahedron.
Certain highly symmetric spaces whose points represent lines in the plane have the shape of a Möbius strip. The many applications of Möbius strips include mechanical belts that wear evenly on both sides, dual-track roller coasters whose carriages alternate between the two tracks, and world maps printed so that antipodes appear opposite each ...
The number of different shapes of the Rubik's Snake is at most 4 23 = 70 368 744 177 664 ( ≈ 7×10 13 or 70 trillion), i.e. 23 turning areas with 4 positions each. The real number of different shapes is lower, since some configurations are spatially impossible (because they would require multiple prisms to occupy the same region ...
The Pyraminx Duo is a puzzle in the shape of a tetrahedron, divided into 4 corner pieces and 4 face centre pieces. Each corner piece has three colours, while the centre pieces each have a single colour. Each face of the puzzle contains one face centre piece and three corner pieces.