In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if
In geometry, the regular icosahedron is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron.
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two solids with such a property: the first solids are the pyramids, cupolas. and a rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. These solids are named after mathematicians Norman Johnson and Victor Zalgaller.
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent regular polygons, and the same number of faces meet at each vertex. There are only five such polyhedra:
In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word stellation comes from the Latin stellātus, "starred", which in turn comes from the Latin stella, "star". Stellation is the reciprocal or dual process to faceting.
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In particular, all its elements or j-faces — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron. It has also been called the kisicosahedron. It was first depicted, in a non-convex form with equilateral triangle faces, by Leonardo da Vinci in Luca Pacioli's Divina proportione, where it was named the icosahedron elevatum. The capsid of the Hepatitis A virus has the shape of a triakis icosahedron.
In geometry, the snub disphenoid is a convex 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 shape also has alternative names called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron; these names mean the 12-sided polyhedron.
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron composed of regular pentagonal faces, three meeting at each vertex. It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler. However, the regular dodecahedron, including the other Platonic solids, has already been described by other philosophers since antiquity.
Spool knitting,loom knitting, corking,French knitting, or tomboy knitting is a form of knitting that uses a spool with a number of nails or pegs around the rim to produce a tube or sheet of fabric. The spool knitting devices are called knitting spools, knitting nancys, knitting frame, knitting loom, or French knitters.
Óc Eo (Vietnamese) is an archaeological site in modern-day Óc Eo commune of Thoại Sơn District in An Giang Province of southern Vietnam. Located in the Mekong Delta, Óc Eo was a busy port of the kingdom of Funan between the 2nd century BC and 12th century AD and it may have been the port known to the Greeks and Romans as Cattigara.
Carved stone balls are petrospheres dated from the late Neolithic, to possibly as late as the Iron Age, mainly found in Scotland, but also elsewhere in Britain and Ireland. They are usually round and rarely oval, and of fairly uniform size at around 2+3⁄4 inches or 7 cm across, with anything between 3 and 160 protruding knobs on the surface. They range from having no ornamentation to extensive and highly varied engraved patterns. A wide range of theories has been produced to explain their use or significance, with none gaining very wide acceptance.
Hypsicles was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and possibly the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.
The icosian game is a mathematical game invented in 1856 by Irish mathematician William Rowan Hamilton. It involves finding a Hamiltonian cycle on a dodecahedron, a polygon using edges of the dodecahedron that passes through all its vertices. Hamilton's invention of the game came from his studies of symmetry, and from his invention of the icosian calculus, a mathematical system describing the symmetries of the dodecahedron.
In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.
Turicum was a Gallo-Roman settlement at the lower end of Lake Zurich, and precursor of the city of Zürich. It was situated within the Roman province of Germania Superior) and near the border to the province of Raetia; there was a tax-collecting point for goods traffic on the waterway Walensee–Obersee-Zürichsee–Limmat–Aare–Rhine.
Cattigara is the name of a major port city located on the Magnus Sinus described by various antiquity sources. Modern scholars have linked Cattigara to the archaeological site of Óc Eo in present-day Vietnam.
