central symmetry

Thus, in the plane central symmetry is the rotation by 180 degrees.

A different measure is the distance skewness, for which a value of zero implies central symmetry.

On the other hand, the tetrahedron does not have central symmetry, so there is no "hemi-tetrahedron".

There is only one case left, the 2-order central symmetry, not to be confused with the axial one.

Spherical polyhedra without central symmetry do not define a projective polyhedron, as the images of vertices, edges, and faces will overlap.

Although the Reuleaux triangle has sixfold dihedral symmetry, the same as an equilateral triangle, it does not have central symmetry.

Non-overlapping projective polyhedra (density 1) correspond to spherical polyhedra (equivalently, convex polyhedra) with central symmetry.

Subgroups of the projective orthogonal group correspond to subgroups of the orthogonal group that contain (that have central symmetry).

Of particular interest are discrete subgroups, which can be realized as symmetries of projective polytopes - these correspond to the (discrete) point groups that include central symmetry.

But if we do, as Tradition demands, once we choose one, the gyration for central symmetry will create 'alias' in another radius, thus creating new distances as a necessity.

In the native form of starch these two types of polymer are organised in granules as alternating semi-crystalline and amorphous layers, the layers in most starches having central symmetry.

Crystal structure of ASIC1 and site-directed mutagenesis studies suggest that ENaC has a central ion channel located along the central symmetry axis in between the three subunits.

The prefix "hemi" is also used to refer to certain projective polyhedra, such as the hemi-cube, which are the image of a 2 to 1 map of a spherical polyhedron with central symmetry.

Since the central symmetry also maps the orthocenter of the reference triangle to that of the Johnson triangle, the homothetic center is also the nine-point center of the Johnson triangle.

In 1976, as part of a student exhibition at the Academy, Struth first showed a grid composed of 49 photographs taken from a centralized perspective on Düsseldorf's deserted streets, each of them obeying a strict logic of central symmetry.

A piezoelectric potential can be created in any bulk or nanostructured semiconductor crystal having non central symmetry, such as the Group III-V and II-VI materials, due to polarization of ions under applied stress and strain.

An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.

There is a 2-to-1 covering map of the sphere to the projective plane, and under this map, projective polyhedra correspond to spherical polyhedra with central symmetry - the 2-fold cover of a projective polyhedron is a centrally symmetric spherical polyhedron.

Buddhists often prostrate before the two objects, although as the glass enclosure and the Buddha statues in the main hall lie on the central symmetry axis of the building, they do so at an angle so that their posteriors are not pointing towards the statue of the Buddha.

In fact, for a plate of circular shape, resting in the centre (or the border, or at least in a set of points with central symmetry), the nodal vibration modes all have central symmetry, so the observation of Jenny is entirely consistent with well-known mathematical properties.

For example, in 3 dimensions, 4 of the 5 Platonic solids have central symmetry (cube/octahedron, dodecahedron/icosahedron), while the tetrahedron does not - however, the stellated octahedron has central symmetry, though the resulting symmetry group is the same as that of the cube/octahedron.