The largest strictly convex deltahedron is the regular icosahedron.The (Archimedean) truncated tetrahedron with its hexagons subdivided into triangles. This figure is not a strictly convex deltahedron, since coplanar (adjacent) faces are not allowed within the definition.
In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all (congruent) equilateral triangles. The name is taken from the Greek upper case delta letter (Δ), which has the shape of an equilateral triangle. There are infinitely many deltahedra. By the handshaking lemma, each deltahedron has an even number of faces. Only eight deltahedra are strictly convex; these have 4, 6, 8, 10, 12, 14, 16, and 20 faces.[1] These eight deltahedra, with their respective numbers of faces, edges, and vertices, are listed below.
^Freudenthal, H; van der Waerden, B. L. (1947), "Over een bewering van Euclides ("On an Assertion of Euclid")", Simon Stevin (in Dutch), 25: 115–128 (They showed that there are just eight strictly convex deltahedra.)
In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all (congruent) equilateral triangles. The name is taken from the Greek...
polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This...
fewest possible faces of any embedded toroidal polyhedron. A toroidal deltahedron was described by John H. Conway in 1997, containing 18 vertices and 36...
names mean a polyhedron with 16 triangular faces. It is an example of deltahedron, and of a Johnson solid. The dual polyhedron of the gyroelongated square...
and 12 vertices. It is an example of the Platonic solid and of the deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron...
faces of triangular bipyramid are equilateral. It is an example of a deltahedron and of a Johnson solid. Many polyhedra are related to the triangular...
names mean a polyhedron with 14 triangular faces. It is an example of a deltahedron and of a Johnson solid. The edges and vertices of the triaugmented triangular...
{4,3}, and the octahedron as {3,4}. Archimedean solid Catalan solid Deltahedron Johnson solid Goldberg polyhedron Kepler-Poinsot polyhedron List of regular...
faces: Sonobe modules can replace each notional edge of the original deltahedron by the central diagonal fold of one unit and each equilateral triangle...
Johnson solids. A polyhedron having regular triangles as faces is called a deltahedron. Euclidean tilings by convex regular polygons Platonic solid List of...
square pyramid. Similarly, the gyroelongated square bipyramid (J17) is a deltahedron (a polyhedron whose faces are all equilateral triangles) constructed...
D-ring Deltoid, the shape that resembles the Greek capital letter Δ Deltahedron Deltoid muscle River delta Delta wing E-shape, the shape that resembles...
pyramids with equilateral triangles are used, the result is a non-convex deltahedron. Any such elevated dodecahedron has the same combinatorial structure...
its dual has all triangular faces, including the snub disphenoid as a deltahedron with all equilateral triangles. However the dual of the snub disphenoid...
triangles. A polyhedron with only equilateral triangles as faces is called a deltahedron. There are only eight different convex deltahedra, one of which is the...
has the same symmetry group as a single octahedron. It is an isohedral deltahedron, meaning that its faces are equilateral triangles and that it has a symmetry...
hypho-, based on whether they represent a complete (closo-) deltahedron, or a deltahedron that is missing one (nido-), two (arachno-) or three (hypho-)...
term is "bisdisphenoid" or "snub disphenoid" as this polyhedron is a deltahedron) [Mo(CN)8]4− in K4[Mo(CN)8]·2H2O Zr in K2[ZrF6] 8 bicapped trigonal prismatic...
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