See also:

• TETRAHEDRON (Gr. riepa-, four, Ebpa, face or base)

TETRAHEDRON (Gr. riepa-, four, Ebpa, See also:

• FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face or See also:

• BASE

base)  , in See also:

• GEOMETRY

geometry, a solid bounded by four triangular faces . It consequently has four vertices and six edges . If the faces be all equal equilateral triangles the solid is termed the " See also:

• REGULAR

regular See also:

• TETRAHEDRON (Gr. riepa-, four, Ebpa, face or base)

tetrahedron . This is one of the Platonic solids, and is treated in the See also:

• ARTICLE (from Lat. articulus, a joint)

article See also:

• POLYHEDRON (Gr. rain, many, ESpa, a base)

POLYHEDRON, as is also the derived Archimedean solid named the " truncated tetrahedron "; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral See also:

• FORM (Lat. forma)

form of the regular See also:

• OCTAHEDRON (Gr. 6K-rw, eight, Mpa, base)

octahedron and consequently a form of the cubic See also:

• SYSTEM

system . The bisphenoids (the hemihedral forms of the tetragonal and rhombic bipyramids), and the trigonal See also:

• PYRAMID

pyramid of the hexagonal system, are examples of non-regular tetrahedra (see See also:

• CRYSTALLOGRAPHY
• CRYSTALLOGRAPHY (from the Gr. Kpbo TaXXO , ice, and -ypachew, to write)

CRYSTALLOGRAPHY) . " See also:

• TETRAHEDRAL

Tetrahedral co-ordinates " are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a See also:

• POSITIVE (or PORTABLE) ORGAN

positive sign being given if the point be between the See also:

• FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face and the opposite vertex, and a negative sign if not . If (u, v, w, t) be the co-ordinates of any point, then the relation u+v+w+t=R, where R is a See also:

• CONSTANT, BENJAMIN (1845-1902)

constant, invariably holds . This system is of much service in following out mathematical, See also:

• PHYSICAL

physical and chemical problems in which it is necessary to represent four variables . Related to the tetrahedron are two See also:

• SPHERES, MUSIC OF THE

spheres which have received much See also:

• ATTENTION (from Lat. ad-tendo, await, expect; the condition of being " stretched " or " tense ")

attention . The " twelve-point See also:

• SPHERE (Gr. vclsa?pa, a ball or globe)

sphere," discovered by P . M . E .

Prouhet {1817-1867) in 1863, is somewhat analogous to the nine-point circle of a triangle . If the perpendiculars from the vertices to the opposite faces of a tetrahedron be concurrent, then a sphere passes through the four feet of the perpendiculars, and consequently through the centre of gravity of each of the four faces, and through the See also:

• MID

mid-points of the segments of the perpendiculars between the vertices and their See also:

• COMMON

common point of intersection . This theorem has been generalized for any tetrahedron; a sphere can be See also:

• DRAWN

drawn through the four feet of the perpendiculars, and consequently through the mid-points of the lines from the vertices to the centre of the hyperboloid having these perpendiculars as generators, and through the orthogonal projections of these points on the opposite faces .