# Tetrahedron Sentence Examples

- The
**tetrahedron**is a particular case. - Related to the
**tetrahedron**are two spheres which have received much attention. - If ABCD is a
**tetrahedron**of reference, any point P in space is determined by an equation of the form (a+13+ - y+5) P = aA+sB +yC +SD: a, a, y, b are, in fact, equivalent to a set of homogeneous coordinates of P. For constructions in a fixed plane three points of reference are sufficient. - "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 positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not. - This usually has the form of a
**tetrahedron**, with its points base occupying the surface of the body of the axis and its apex pointing towards the interior. - In the stem, segments are successively cut off from the sides of the
**tetrahedron**, and b~ their subsequent division the body of the stem is produced. - Assuming the four valencies of the carbon atom to be directed from the centre of a regular
**tetrahedron**towards its four corners, the angle at which they meet. - We may therefore regard the nitrogen atoms as occupying the centres of a cubic space lattice composed of iodine atoms, between which the hydrogen atoms are distributed on the
**tetrahedron**face normals. - The
**tetrahedron**is a particular case. - For a
**tetrahedron**, two of whose opposite edges are AB and CD, we require the area of the section by a plane parallel to AB and CD. - If this be so the form of the diamond is really the
**tetrahedron**(and the various figures derived symmetrically from it) and not the octadehron. - If the grooves be left out of account, the large faces which have replaced each
**tetrahedron**corner then make up a figure which has the aspect of a simple octahedron. - R shows a combination of two tetrahedra, in which the four faces of one
**tetrahedron**are larger than the four faces of the other; further, the two sets of faces differ in surface FIG. - Again, if G be the mass-centre of four particles a, $, 7, situate at the vertices of a
**tetrahedron**ABCD, we find a: ~ :~: tet GBCD: tetUGCDA: tetGDAB: tetGABC, and by suitable determination of the ratios on the left hand we can make G assume any assigned position in space. - If a+$+y+~=O, G is at infinity; if a = fi =~ =~, G bisects the lines joining the middle points of opposite edges of the
**tetrahedron**ABCD; if a: ~: 7: = M3CD: z~CDA: ~DAB: L~ABC, G is at the centre of the inscribed sphere. - As particular cases: the mass-centre of a uniform thin triangular plate coincides with that of three equal particles at the corners; and that of a uniform solid
**tetrahedron**coincides with that of four equal particles at the vertices. - If four fluids, a, b, c, d, meet in a point 0, and if a
**tetrahedron**AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this**tetrahedron**so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the**tetrahedron**will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the**tetrahedron**will be normal to the tangent planes at 0 to the other five surfaces of contact. - If six films of the same liquid meet in a point the corresponding
**tetrahedron**is a regular**tetrahedron**, and each film, where it meets the others, has an angle whose cosine is - i. - The names of these five solids are: (r) the
**tetrahedron**, enclosed by four equilateral triangles; (2) the cube or hexahedron, enclosed by 6 squares; (3) the octahedron, enclosed by 8 equilateral triangles; (4) the dodecahedron, enclosed by 12 pentagons; (5) the icosahedron, enclosed by 20 equilateral triangles. - These solids played an important part in the geometry of the Pythagoreans, and in their cosmology symbolized the five elements: fire (
**tetrahedron**), air (octahedron), water (icosahedron), earth (cube), universe or ether (dodecahedron). - The truncated
**tetrahedron**is formed by truncating the vertices of a regular**tetrahedron**so as to leave the original faces hexagons. - We may also note that of the Archimedean solids: the truncated
**tetrahedron**, truncated cube, and truncated dodecahedron, are the reciprocals of the crystal forms triakistetrahedron, triakisoctahedron and triakisicosahedron. - Since the
**tetrahedron**is the hemihedral form of the octahedron, and the octahedron and cube are reciprocal, we may term these two latter solids " reciprocal holohedra " of the**tetrahedron**. - The equilateral triangle is the basis of the
**tetrahedron**, octahedron and icosahedron.' - It is readily seen that the
**tetrahedron**is its own reciprocal, i.e. - Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a
**tetrahedron**, with one edge in the surface.