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In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties.
An unsolved Tentai Show puzzle. The same puzzle, solved. The regions are colored to reveal a picture of a cat. Tentai Show (Japanese: 天体ショー tentai shō), also known by the names Tentaisho, Galaxies, Spiral Galaxies, or Sym-a-Pix, is a binary-determination logic puzzle published by Nikoli.
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]
A pentomino (or 5-omino) is a polyomino of order 5; that is, a polygon in the plane made of 5 equal-sized squares connected edge to edge. The term is derived from the Greek word for '5' and "domino". When rotations and reflections are not considered to be distinct shapes, there are 12 different free pentominoes.
The Symmetries of Things has three major sections, subdivided into 26 chapters. [8] The first of the sections discusses the symmetries of geometric objects. It includes both the symmetries of finite objects in two and three dimensions, and two-dimensional infinite structures such as frieze patterns and tessellations, [2] and develops a new notation for these symmetries based on work of ...
A Sudoku with 24 clues, dihedral symmetry (a 90° rotational symmetry, which also includes a symmetry on both orthogonal axis, 180° rotational symmetry, and diagonal symmetry) is known to exist, but it is not known if this number of clues is minimal for this class of Sudoku. [5]
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
symmetry with respect to both grid line directions, and hence also 2-fold rotational symmetry: D 2 (2) (also known as the Klein four-group) symmetry with respect to both diagonal directions, and hence also 2-fold rotational symmetry: D 2 (7) 4-fold rotational symmetry: C 4 (8) 1 fixed polyomino for each free polyomino: all symmetry of the ...