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Rheinfelden, Switzerland
Rheinfelden is a city and municipality of the canton of Aargau in Switzerland, seat of the district of Rheinfelden. It is east of Basel. The name means the fields of the Rhine, as the town is on the Hochrhein. It is home to Feldschlösschen, the most popular beer in Switzerland. The city is across the river from Rheinfelden in Baden-Württemberg; the two cities were joined until Napoleon Bonaparte fixed the German–Swiss border on the Rhine in 1802 and are still socially and economically tied.
The old town of Rheinfelden is on the Rhine river. The Rhine can be traveled down by ship from Rheinfelden all the way to the North Sea.
The area around Rheinfelden was already settled about 10,000 years ago. At that time, people lived in the "Hermitage", a small natural cave next to the current highway. In the year 45 BC, a few kilometers west, the village Augusta Raurica was made, the first Roman town in Switzerland, near modern Kaiseraugst. Towards the end of the 4th century, a fort was built at the western settlement.
During the 17th century, there was very little time during which the city enjoyed peace. During the Rappenkrieg (a peasant uprising that lasted from 1612 until 1614), the city was ruined. Between 1633 and 1638, the Thirty Years' War reached Fricktal, where Rheinfelden played a big role. On 15 July 1633, Swedish and French troops ruined the city. On 5 February 1638, the city was put under attack by Protestant troops sent by Bernhard of Saxe-Weimar. On 28 February, the Battle of Rheinfelden began, as the city was attacked by the bigger Imperial and Bavarian troops sent by Johann von Werth and Federigo Savelli. The Protestants lost this battle and moved on. Bernhard brought them weapons, but in the second passage on 3 March they were defeated, as he and his men unexpectedly re-appeared on the battlefield, with Savelli and Werth falling into captivity.
By the end of the Thirty Years' War, the Austrians had built a fortress on the island to secure the southwestern border of the Breisgau. In 1678, French troops sent by François de Créquy fired at the city. In 1745, during the War of the Austrian Succession, the French made a fortress on the same ground and also ruined part of the city wall. On 17 July 1796, Rheinfelden was again occupied and looted by the French.
Because of the Treaty of Campo Formio in 1797, the Fricktal became a protectorate of the French, making the front line between the French Revolutionary and the Austrian troops in the War of the Second Coalition. On 20 February 1802, Rheinfelden was made the capital city of the new Canton of Fricktal, joining the Helvetic Republic in August, the point at which the city became mostly Swiss. The seat of the cantonal government was here instead of in Laufenburg. With the beginning of the "Reichsdeputationshauptschluss" (the German Mediatisation), Napoleon Bonaparte removed the canton of Fricktal. Since 19 March 1803, Rheinfelden has been the capital of the district of the same name, in the canton of Aargau.
Klickitat
The Klickitat (also spelled Klikitat) are a Native American tribe of the Pacific Northwest. A Shahaptian tribe, their neighbors to the east were the Yakama, who speak a closely related language. Their neighbors to the west are the Salishan and Chinookan tribes. Their name has been used for naming places like Klickitat County, Washington, Klickitat, Washington, and the Klickitat River, a tributary of the Columbia River.
Arzo
Arzo was a municipality of the district Mendrisio in the canton of Ticino in Switzerland. On 5 April 2009 the former municipalities of Arzo, Capolago, Genestrerio, Mendrisio, Rancate and Tremona merged into the municipality of Mendrisio.
Ascona
Ascona is a municipality of the district of Locarno in the canton of Ticino in Switzerland.
Astano
Astano is a municipality of the district of Lugano in the canton of Ticino in Switzerland.
Lugano (district)
Lugano is a district of the canton of Ticino in Switzerland.
The district of Lugano has 98 municipalities divided in 12 circles:
Locarno (district)
Locarno is a district of the canton of Ticino in Switzerland.
The district of Locarno has 40 municipalities divided in 7 circles:
Vallemaggia (district)
Vallemaggia is a district of the canton of Ticino in Switzerland. The capital city of the district is Cevio.
Bellinzona (district)
Bellinzona is a district of the canton of Ticino in Switzerland.
Riviera (district)
Riviera is a district of the canton of Ticino in Switzerland. The capital city of the district is Biasca.
Blenio (district)
Blenio is a district of the canton of Ticino in Switzerland. The capital city of the district is Acquarossa.
Leventina (district)
Leventina is a district of the canton of Ticino in Switzerland. The capital city of the district is Faido.
Sapir-Whorf hypothesis
The Sapir–Whorf hypothesis is a linguistic idea which claims that the language people speak changes the way they think and act.
Icosahedron
An icosahedron is a Platonic solid that is made of triangles and has twenty sides.
There are many kinds of icosahedra, with some being more symmetrical than others. The best known is the Platonic, convex regular icosahedron.
There are two objects, one convex and one concave, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a "great icosahedron".
The convex regular icosahedron is usually referred to simply as the "regular icosahedron", one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.
Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal faces around each vertex.
The great icosahedron is one of the four regular star Kepler-Poinsot polyhedra. Its Schläfli symbol is {3, }. Like the convex form, it also has 20 equilateral triangle faces, but its vertex figure is a pentagram rather than a pentagon, leading to geometrically intersecting faces. The intersections of the triangles do not represent new edges.
Its dual polyhedron is the great stellated dodecahedron (, 3), having three regular star pentagonal faces around each vertex.
Stellation is the process of extending the faces or edges of a polyhedron until they meet to form a new polyhedron. It is done symmetrically so that the resulting figure retains the overall symmetry of the parent figure.
In their book "The Fifty-Nine Icosahedra", Coxeter et al. enumerated 58 such stellations of the regular icosahedron.
Of these, many have a single face in each of the 20 face planes and so are also icosahedra. The great icosahedron is among them.
Other stellations have more than one face in each plane or form compounds of simpler polyhedra. These are not strictly icosahedra, although they are often referred to as such.
Octahedron
An Octahedron is a polyhedron made of eight faces. in the case of the regular octahedron, these faces are triangles. The ocahedron looks like two pyramids, which share the same base.
In chemistry, octahedra are common: diamonds and fluorite are examples of crystals that are octahedra.
If the edge length of a regular octahedron is "a", the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is
and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is
while the midradius, which touches the middle of each edge, is
The "octahedron" has four special orthogonal projections, centered, on an edge, vertex, face, and normal to a face. The second and third correspond to the B and A Coxeter planes.