How to use Tetrahedron in a sentence

tetrahedron
  • Related to the tetrahedron are two spheres which have received much attention.

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  • If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.

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  • The faces of the cube are striated parallel to one diagonal, and alternate corners are sometimes replaced by faces of a tetrahedron.

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  • The fundamental form is the tetrahedron.

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  • The base of the tetrahedron is a stiffened steel grillage that will incorporate the connection to the bearing below.

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  • Finite generalized tetrahedron groups with a cubic relator 2003/21 Vincent Schmitt.

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  • The puzzle is to arrange these six pieces on a triangular wooden base to make a tetrahedron.

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  • When the strands are heated in a salt solution to just below boiling point then rapidly cooled they bond together to form a tetrahedron.

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  • And there you've got another tetrahedron, and it's upside down.

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  • Volume of a tetrahedron What is the volume of a regular tetrahedron with edges one unit long?

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Volume of a Tetrahedron What is the volume of a regular tetrahedron with edges one unit long?

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • A scalene triangle abc might also be employed, or a tetrahedron.

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  • The tetrahedron is a particular case.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

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  • The truncated tetrahedron is formed by truncating the vertices of a regular tetrahedron so as to leave the original faces hexagons.

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  • It is readily seen that the tetrahedron is its own reciprocal, i.e.

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  • 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.

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  • 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.

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  • 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.

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