How to use Tetrahedron in a sentence
Related to the tetrahedron are two spheres which have received much attention.
If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.
The faces of the cube are striated parallel to one diagonal, and alternate corners are sometimes replaced by faces of a tetrahedron.
The fundamental form is the tetrahedron.
The base of the tetrahedron is a stiffened steel grillage that will incorporate the connection to the bearing below.Advertisement
Finite generalized tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.
The puzzle is to arrange these six pieces on a triangular wooden base to make a tetrahedron.
When the strands are heated in a salt solution to just below boiling point then rapidly cooled they bond together to form a tetrahedron.
And there you've got another tetrahedron, and it's upside down.
Volume of a tetrahedron What is the volume of a regular tetrahedron with edges one unit long?Advertisement
This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.
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 mid-points of the segments of the perpendiculars between the vertices and their common point of intersection.
This theorem has been generalized for any tetrahedron; a sphere can be 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.
The " tetrahedral theory " brought forward by Lowthian Green,' that the form of the earth is a spheroid based on a regular tetrahedron, is more serviceable, because it accounts for three very interesting facts of the terrestrial plan - (1) the antipodal position of continents and ocean basins; (2) the tri angular outline of the continents; and (3) the excess of sea in the southern hemisphere.
The right-hand expression is six times the volume of the tetrahedron of which the lines AA, BB representihg the forces are opposite edges; and we infer that, in whatever way the wrench be resolved into two forces, the volume of this tetrahedron is invariable.Advertisement
For instance, considering four equal particles at the vertices of a regular tetrahedron, we can infer that the radius R of the circumscribing sphere is given by R2=j a2, if a be the length of an edge.
Volume of a Tetrahedron What is the volume of a regular tetrahedron with edges one unit long?
A variety of three-dimensional shapes, such as the tetrahedron, cube, and diamond featured in Dollar Bill Origami and hearts and stars at the Origami Resource Center.
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.
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.Advertisement
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.
A scalene triangle abc might also be employed, or a tetrahedron.
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.Advertisement
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.
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 equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'
The truncated tetrahedron is formed by truncating the vertices of a regular tetrahedron so as to leave the original faces hexagons.
It is readily seen that the tetrahedron is its own reciprocal, i.e.Advertisement
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.
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.
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.