In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the 5 Platonic solids and excluding the prisms and antiprisms, they differ from the Johnson solids, whose regular polygonal faces do not meet in identical vertices. "Identical vertices" means that each two vertices are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid directly on its initial position. Branko Grünbaum observed that a 14th polyhedron, the elongated square gyrobicupola, meets a weaker definition of an Archimedean solid, in which "identical vertices" means that the faces surrounding each vertex are of the same types, so only a local isometry is required. Grünbaum pointed out a frequent error in which authors define Archimedean solids using this local definition but omit the 14th polyhedron. If only 13 polyhedra are to be listed, the definition must use global symmetries of the polyhedron rather than local neighborhoods.
Prisms and antiprisms, whose symmetry groups are the dihedral groups, are not considered to be Archimedean solids though their faces are regular polygons and their symmetry groups act transitively on their vertices. Excluding these two infinite families, there are 13 Archimedean solids. All the Archimedean solids can be made via Wythoff constructions from the Platonic solids with tetrahedral and icosahedral symmetry; the Archimedean solids take their name from Archimedes. Pappus refers to it. During the Renaissance and mathematicians valued pure forms with high symmetry, by around 1620 Johannes Kepler had completed the rediscovery of the 13 polyhedra, as well as defining the prisms and the non-convex solids known as Kepler-Poinsot polyhedra; the reader may find more information about the rediscovery of the Archimedean solids during the renaissance in the paper by Peter Schreiber et al. published in 2008. Kepler may have found the elongated square gyrobicupola: at least, he once stated that there were 14 Archimedean solids.
However, his published enumeration only includes the 13 uniform polyhedra, the first clear statement of the pseudorhombicuboctahedron's existence was made in 1905, by Duncan Sommerville. There are 13 Archimedean solids. Here the vertex configuration refers to the type of regular polygons. For example, a vertex configuration of means that a square and octagon meet at a vertex; some definitions of semiregular polyhedron include one more figure, the elongated square gyrobicupola or "pseudo-rhombicuboctahedron". The number of vertices is 720° divided by the vertex angle defect; the cuboctahedron and icosidodecahedron are called quasi-regular. The duals of the Archimedean solids are called the Catalan solids. Together with the bipyramids and trapezohedra, these are the face-uniform solids with regular vertices; the snub cube and snub dodecahedron are known as chiral, as they come in a left-handed form and right-handed form. When something comes in multiple forms which are each other's three-dimensional mirror image, these forms may be called enantiomorphs..
The different Archimedean and Platonic solids can be related to each other using a handful of general constructions. Starting with a Platonic solid, truncation involves cutting away of corners. To preserve symmetry, the cut is in a plane perpendicular to the line joining a corner to the center of the polyhedron and is the same for all corners. Depending on how much is truncated, different Platonic and Archimedean solids can be created. If the truncation is deep enough such that each pair of faces from adjacent vertices shares one point, it is known as a rectification. An expansion, or cantellation, involves moving each face away from the center and taking the convex hull. Expansion with twisting involves rotating the faces, thus splitting each rectangle corresponding to an edge into two triangles by one of the diagonals of the rectangle; the last construction we use here is truncation of both edges. Ignoring scaling, expansion can be viewed the rectification of the rectification; the cantitruncation can be viewed as the truncation of the rectification.
Note the duality between the cube and the octahedron, between the dodecahedron and the icosahedron. Because the tetrahedron is self-dual, only one Archimedean solid that has at most tetrahedral symmetry. Aperiodic tiling Archimedean graph List of uniform polyhedra Prince Rupert's cube#Generalizations Toroidal polyhedron Quasicrystal Semiregular polyhedron Regular polyhedron Uniform polyhedron Icosahedral twins G
Carlow County Museum is a county museum documenting the history of County Carlow. Located on College Street in Carlow town, the building was the Presentation Convent which houses the Carlow Library and Archives; the Museum was founded by the Carlow Historical & Archaeological Society the Old Carlow Society, in 1973 and was run by the Society on a voluntary basis until 2002. The collections were housed first in the old Christian Brothers' building, latterly the former theatre room of the Town Hall from 1979; the Museum was reopened in the redeveloped convent building in 2012, the last of the buildings to open in this new cultural quarter. It is now operated by Carlow Town Council and Carlow County Council in association with the CHAS; the Museum consists of four exhibition rooms housing temporary displays. The diverse collection includes objects that cover the archaeological, social history and folk life of the local area, it is designated to collect archaeological finds by the National Museum of Ireland.
One of the most notable objects on display is the 19th century pulpit from Carlow Cathedral, included in The Irish Times A History of Ireland in 100 Objects. Other notable objects in the Museum's collections pertain to John Tyndall, Kevin Barry, Captain Myles Kehoe, the Carlow Sugar Factory; the Museum has unveiled a new installation as part of the Ireland 2016 Centenary Programme, the'Carlow 1916 Commemorative Stained Glass Panel by Peadar Lamb' depicts a Carlow narrative on the 1916 Rising, featuring some of the key Carlow figures and the role they played in 1916. On view is a special exhibition about St. Willibrord titled: Saint Willibrord, Patron Saint of Luxembourg and his County Carlow Connection; the museum has full Wheelchair Access. September–May: Mon–Sat: 10.00am – 4.30pm June–August: Mon–Sat: 10.00am – 5.00pm Sun & Bank Holidays: 2.00pm – 4.30pm Last admission half hour before closing. Oak Park, County Carlow Carlow County Museum Carlow Historical and Archaeological Society - Museum History Carlow Tourism Carlow Military Museum Discover Ireland
Eric Collins is a play-by-play sports announcer the voice of the NBA's Charlotte Hornets on Fox Sports South. From 2009 through 2013, Collins served as the part-time television voice of the Los Angeles Dodgers, taking over the duties of Dodger radio voice Charley Steiner, the team's play-by-play announcer on road telecasts east of Denver. Collins' broadcasting experience includes play-by-play for NBC Sports' coverage of the USA Baseball team during the Beijing 2008 Summer Olympics, as well as calling ESPN's coverage of college football, college basketball, college baseball and softball Super Regional tournaments and Women's College World Series games, he worked as a sideline reporter for Chicago Bulls broadcasts from 1997 to 2002. Collins has broadcast every game of the World Cup of Softball on ESPN since its inception in 2005, with partner Michele Smith. In August 2010, the Big Ten Network announced that Collins would handle play-by-play duties in college football and basketball, he does play-by-play announcing for Fox College Hoops.
He was the announcer for the famous Stephen F. Austin Lumberjacks men's basketball's win over Duke in Cameron Indoor Stadium on November 26, 2019, his call for the buzzer beating layup by Nathan Bain was "BAAAIINNN... YES! THE LUMBERJACKS HAVE DONE IT!"On August 27, 2015, Collins was named the new television play-by-play announcer for the Charlotte Hornets, replacing Steve Martin, who will return to his original role as the team's radio play-by-play voice. Collins will be joined by former Hornet Dell Curry and Stephanie Ready, the NBA's first full-time female analyst. Collins is a graduate of St. Lawrence Syracuse University. Dodgers.com: Eric Collins to join Dodger broadcast team in 2009 Dodgers.com Broadcasters list: Eric Collins' bio Dodgers' Eric Collins adds Big Ten football to his announcing chores