A tic is a sudden, repetitive, nonrhythmic motor movement or vocalization involving discrete muscle groups. Tics can be invisible to the observer, such as abdominal tensing or toe crunching. Common motor and phonic tics are, respectively, eye blinking and throat clearing.
Tics are classified as either motor or phonic, and simple or complex.
Motor or phonic
Motor tics are movement-based tics affecting discrete muscle groups.
Phonic tics are involuntary sounds produced by moving air through the nose, mouth, or throat. They may be alternately referred to as verbal tics or vocal tics, but most diagnosticians prefer the term phonic tics to reflect the notion that the vocal cords are not involved in all tics that produce sound.
The tongue-in-cheekfigure of speech is used to imply that a statement or other production is humorously or otherwise not seriously intended, and it should not be taken at face value. The facial expression typically indicates that one is joking or making a mental effort. In the past, it may also have indicated contempt, but that is no longer common.
By 1842, the phrase had acquired its contemporary meaning, indicating that a statement was not meant to be taken seriously. Early users of the phrase include Sir Walter Scott in his 1828 The Fair Maid of Perth.
If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and .
Area and volume
The area A and the volumeV of a truncated cube of edge length a are:
The truncated cube has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: triangles, and octagons. The last two correspond to the B2 and A2Coxeter planes.
The truncated cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.