The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. consider a tetrahedron centered (0,0,0), oriented with z axis along a fourfold (c 3) rotational symmetry axis, and with one of the top three edges lying in the xz plane (left figure). in this figure, vertices are shown in black, face. In general, a tetrahedron is a polyhedron with four sides. if all faces are congruent, the tetrahedron is known as an isosceles tetrahedron. if all faces are congruent to an equilateral triangle, then the tetrahedron is known as a regular tetrahedron (although the term "tetrahedron" without further qualification is often used to mean "regular tetrahedron"). a tetrahedron having a trihedron all.
The regular tetrahedron, often simply called "the" tetrahedron, is the platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral triangular faces, 4{3}. it is illustrated above together with a wireframe version and a net that can be used for its construction. the regular tetrahedron is also the uniform polyhedron with maeder index 1 (maeder 1997. The reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three dimensional solid common to four spheres of equal radius placed so that the center of each sphere lies on the surface of the other three. the centers of the spheres are therefore located at the vertices of a regular tetrahedron, and the solid consists of an "inflated" tetrahedron with four curved edges. "the" tetrahedral graph is the platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph k 4 and therefore also the wheel graph w 4. it is implemented in the wolfram language as graphdata["tetrahedralgraph"]. the tetrahedral graph has a single minimal integral embedding, illustrated above (harborth and möller 1994), with maximum edge length 4. the. The platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. there are exactly five such solids (steinhaus 1999, pp. 252 256): the cube, dodecahedron, icosahedron, octahedron, and tetrahedron, as was proved by euclid in the last proposition of the elements. the platonic solids are sometimes.
"the" tetrahedral graph is the platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph k 4 and therefore also the wheel graph w 4. it is implemented in the wolfram language as graphdata["tetrahedralgraph"]. the tetrahedral graph has a single minimal integral embedding, illustrated above (harborth and möller 1994), with maximum edge length 4. the. The platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. there are exactly five such solids (steinhaus 1999, pp. 252 256): the cube, dodecahedron, icosahedron, octahedron, and tetrahedron, as was proved by euclid in the last proposition of the elements. the platonic solids are sometimes. Represents a collection of tetrahedra. details and options. is also known as regular tetrahedron or triangular pyramid. can be used as a geometric region and as a graphics primitive. represents the region consisting of all the convex combinations of corner points. can be used to convert a tetrahedron to an explicit. A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. the reuleaux triangle has the smallest area for a given width of any curve of constant width. let the arc radius be r. since the area of each meniscus shaped portion of the reuleaux triangle is a circular segment with opening angle theta=pi 3, a s = 1 2r^2.
Represents a collection of tetrahedra. details and options. is also known as regular tetrahedron or triangular pyramid. can be used as a geometric region and as a graphics primitive. represents the region consisting of all the convex combinations of corner points. can be used to convert a tetrahedron to an explicit. A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. the reuleaux triangle has the smallest area for a given width of any curve of constant width. let the arc radius be r. since the area of each meniscus shaped portion of the reuleaux triangle is a circular segment with opening angle theta=pi 3, a s = 1 2r^2.
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