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An American-style 15×15 crossword grid layout. A crossword (or crossword puzzle) is a word game consisting of a grid of black and white squares, into which solvers enter words or phrases ("entries") crossing each other horizontally ("across") and vertically ("down") according to a set of clues. Each white square is typically filled with one ...
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]
Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern.
Nearly all the Times crossword grids have rotational symmetry: they can be rotated 180 degrees and remain identical. Rarely, puzzles with only vertical or horizontal symmetry can be found; yet rarer are asymmetrical puzzles, usually when an unusual theme requires breaking the symmetry rule.
The proper rotations, (order-3 rotation on a vertex and face, and order-2 on two edges) and reflection plane (through two faces and one edge) in the symmetry group of the regular tetrahedron The regular tetrahedron has 24 isometries, forming the symmetry group known as full tetrahedral symmetry T d {\displaystyle \mathrm {T} _{\mathrm {d} }} .
Antipodal symmetry is an alternative name for a point reflection symmetry through the origin. [14] Such a "reflection" preserves orientation if and only if k is an even number. [15] This implies that for m = 3 (as well as for other odd m), a point reflection changes the orientation of the space, like a mirror-image symmetry.
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Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object