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Like kites, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent. Any non-self-crossing quadrilateral that has an axis of symmetry must be either a kite, with a diagonal axis of symmetry; or an isosceles trapezoid, with an axis of
Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...
In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right ...
The triangles with reflection symmetry are isosceles, the quadrilaterals with this symmetry are kites and isosceles trapezoids. [11] For each line or plane of reflection, the symmetry group is isomorphic with C s (see point groups in three dimensions for more), one of the three types of order two (involutions), hence algebraically isomorphic to ...
A high-index reflective subgroup is the prismatic octahedral symmetry, [4,3,2] (), order 96, subgroup index 4, (Du Val #44 (O/C 2;O/C 2) *, Conway ± 1 / 24 [O×O].2). The truncated cubic prism has this symmetry with Coxeter diagram and the cubic prism is a lower symmetry construction of the tesseract, as .
The kite is a quadrilateral whose four interior angles are 72, 72, 72, and 144 degrees. The kite may be bisected along its axis of symmetry to form a pair of acute Robinson triangles (with angles of 36, 72 and 72 degrees). The dart is a non-convex quadrilateral whose four interior angles are 36, 72, 36, and 216 degrees. The dart may be bisected ...
The symmetry group of a square belongs to the family of dihedral groups, D n (abstract group type Dih n), including as many reflections as rotations. The infinite rotational symmetry of the circle implies reflection symmetry as well, but formally the circle group S 1 is distinct from Dih(S 1) because the latter explicitly includes the reflections.
The infinite series of axial or prismatic groups have an index n, which can be any integer; in each series, the nth symmetry group contains n-fold rotational symmetry about an axis, i.e. symmetry with respect to a rotation by an angle 360°/n. n=1 covers the cases of no rotational symmetry at all.