tetrahedron

geometry

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July 14, 2026

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A tetrahedron is a geometric solid with four faces. It is the simplest type of polyhedron, which is a three-dimensional object made of polygonal surfaces. The faces of a tetrahedron are typically triangles.12

A tetrahedron is also one of the five Platonic solids, which are regular polyhedra where all faces are identical regular polygons and all angles are the same. The other Platonic solids are the cube, octahedron, dodecahedron, and icosahedron. Historically, the tetrahedron has been associated with the element fire.3

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clay mineral
General features
These features are continuous two-dimensional tetrahedral sheets of composition Si₂O₅, with SiO₄ tetrahedrons (Figure 1) linked by the sharing of three corners of each tetrahedron to form a hexagonal mesh pattern (Figure 2A). Frequently, silicon atoms of the tetrahedrons are partially substituted for by aluminum and, to a lesser extent,…
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These features are continuous two-dimensional tetrahedral sheets of composition Si₂O₅, with SiO₄ tetrahedrons (Figure 1) linked by the sharing of three corners of each tetrahedron to form a hexagonal mesh pattern (Figure 2A). Frequently, silicon atoms of the tetrahedrons are partially substituted for by aluminum and, to a lesser extent,…
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inorganic polymer
Silicates
…found at the centres of tetrahedrons with oxygen atoms at the corners. The silicon is always tetravalent (i.e., has an oxidation state of +4). The variation in the silicon-to-oxygen ratio occurs because the silicon-oxygen tetrahedrons may exist as discrete, independent units or may share oxygen atoms at corners, edges, or—in…
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…found at the centres of tetrahedrons with oxygen atoms at the corners. The silicon is always tetravalent (i.e., has an oxidation state of +4). The variation in the silicon-to-oxygen ratio occurs because the silicon-oxygen tetrahedrons may exist as discrete, independent units or may share oxygen atoms at corners, edges, or—in…
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R. Buckminster Fuller
Life
…of this system is the tetrahedron (a pyramid shape with four sides, including the base), which, in combination with octahedrons (eight-sided shapes), forms the most economic space-filling structures. The architectural consequence of the use of this geometry by Fuller was the geodesic dome, a frame the total strength of which…
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…of this system is the tetrahedron (a pyramid shape with four sides, including the base), which, in combination with octahedrons (eight-sided shapes), forms the most economic space-filling structures. The architectural consequence of the use of this geometry by Fuller was the geodesic dome, a frame the total strength of which…
Read More