Information AboutTetrahedron |
| CATEGORIES ABOUT TETRAHEDRON | |
| deltahedra | |
| platonic solids | |
| regular polyhedra | |
| polyhedra | |
| self-dual polyhedra | |
| prismatoid polyhedra | |
| pyramids and bipyramids | |
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A tetrahedron (plural: '''tetrahedra''') is a Polyhedron composed of four Triangular faces, three of which meet at each Vertex . A '''regular tetrahedron''' is one in which the four triangles are regular, or "equilateral," and is one of the Platonic Solid s. __TOC__ Like all Convex polyhedra, a tetrahedron can be folded from a single sheet of paper. SURFACE AREA AND VOLUME The surface area ''A'' and the volume ''V'' of a regular tetrahedron of edge length ''a'' are : : The height is , the angle between an edge and a face is arctan (ca. 55°), and between two faces (ca. 71°). Note that with respect to the base plane the Slope of a face is twice that of an edge, corresponding to the fact that the horizontal distance covered from the base to the Apex along an edge is twice that in a face, from the midpoint at the base. Like for any pyramid, the volume is where ''A'' is the area of the base and ''h'' the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apexes to the opposite faces are inversely proportional to the areas of these faces. Also, for a tetrahedron ''ABCT'' the volume is given by : where ''a'' is angle ''ATB'', ''b'' is angle ''BTC'', and ''c'' is angle ''CTA''. Any two opposite edges of a tetrahedron lie on two Skew Lines . If the closest pair of points between these two lines are points in the edges, they define the distance between the edges; otherwise, the distance between the edges equals that between one of the endpoints and the opposite edge. | ||
| : <math>V | rac { (\mathbf{d}-\mathbf{a}) \cdot ((\mathbf{d}-\mathbf{b}) imes (\mathbf{d}-\mathbf{c})) } {6}</math> {Link without Title} |
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| Image:Truncatedtetrahedronjpg | "http://wwwinformationdelightinfo/information/entry/Truncated_tetrahedron" class="copylinks">Truncated Tetrahedron |
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| Image:Stella Octangulapng | "http://wwwinformationdelightinfo/information/entry/Stella_octangula" class="copylinks">Two Tetrahedra In A Cube |
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| Image:Compound Of Five Tetrahedrapng | "http://wwwinformationdelightinfo/information/entry/Compound_of_five_tetrahedra" class="copylinks">Compound Of Five Tetrahedra |
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| Image:Compound Of Ten Tetrahedrapng | "http://wwwinformationdelightinfo/information/entry/Compound_of_ten_tetrahedra" class="copylinks">Compound Of Ten Tetrahedra |
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