Instruct: Given a question, retrieve relevant passages that answer the question.
Query: When was the Pentagon built?
The building was designed by American architect George Bergstrom and built by contractor John McShain. Ground was broken on September 11, 1941, and the building was dedicated on January 15, 1943. General Brehon Somervell provided the major motivating power behind the project;[5] Colonel Leslie Groves was responsible for overseeing the project for the U.S. Army.
When triskelia assemble together in solution, they can interact with enough flexibility to form 6-sided rings (hexagons) that yield a flat lattice, or 5-sided rings (pentagons) that are necessary for curved lattice formation. When many triskelions connect, they can form a basket-like structure. The structure shown, is built of 36 triskelia, one of which is shown in blue. Another common assembly is a truncated icosahedron. To enclose a vesicle, exactly 12 pentagons must be present in the lattice.
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The "n"th pentagonal number "p" is the number of "distinct" dots in a pattern of dots consisting of the "outlines" of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of the 10 – leaving 12 distinct dots, 10 in the form of a pentagon, and 2 inside.
Following the September 11 attacks, SR 110 was closed to trucks and tour buses due to its proximity to the Pentagon. Police checkpoints were staffed around the clock to enforce this restriction. In September 2002, a contract was awarded to reroute SR 110 to increase the standoff distance between vehicles and the Pentagon. The project, called the Pentagon Secure Bypass, was completed in 2004. SR 110 was shifted eastward in a long arc to maintain a buffer distance from the Pentagon and a two-lane bridge to provide access to the Pentagon North parking lot and two pedestrian bridges were built over the new route. These and related security improvements cost $35 million (equivalent to $ in 2021) and were completed in October 2004.
To keep the Pentagon operational at all times during renovation, one fifth of the building's 25,000 occupants must be relocated to swing space, temporary office space in and around the Pentagon. The vacated "wedge" of the Pentagon is then sealed off for demolition and abatement.
Over of external swing space was built-out in nearby Rosslyn and Crystal City. Over 45 floors of office space had to be connected to the Pentagon's voice and data communications systems.
Wedge 1 was the first above-ground section of the Pentagon to undergo renovation. Demolition of the existing structure and hazardous material abatement began in 1998, and the first move-in of tenants occurred in February 2001. The last tenants moved in on February 6, 2003.
The first of the two trails built was the easternmost section from the Mt Vernon trail to Columbia Pike. It runs 1.2 miles through Lady Bird Johnson Park and then along the edge of the Pentagon and the National 9/11 Pentagon Memorial. The trail section was first proposed in 1993 but it took decades to complete. The first section, from Memorial Circle to the existing sidewalks along the Pentagon grounds was completed in the late 1990s. In 2006, as part of a renovation of the Pentagon following 9/11, a section was built adjacent to the new security wall. Another section along the Pentagon Memorial was built in conjunction with that project and opened in September 2008. From 2015 to 2018, VDOT rebuilt the Washington Boulevard Bridge over Route 27 and when they did, they built the section of trail from the Pentagon parking lot ramp to the security wall section built in 2006. At the same time they built a short section from the Pentagon Memorial to Columbia Pike. That work was completed in December 2017.
But now, the interaction energy is supposed to be at a minimum when atoms sit on the vertices of a regular pentagon. Trying to propagate in the long range a packing of these pentagons sharing edges (atomic bonds) and vertices (atoms) is impossible. This is due to the impossibility of tiling a plane with regular pentagons, simply because the pentagon vertex angle does not divide 2. Three such pentagons can easily fit at a common vertex, but a gap remains between two edges. It is this kind of discrepancy which is called "geometric frustration". There is one way to overcome this difficulty. Let the surface to be tiled be free of any presupposed topology, and let us build the tiling with a strict application of the local interaction rule. In this simple example, we observe that the surface inherits the topology of a sphere and so receives a curvature. The final structure, here a pentagonal dodecahedron, allows for a perfect propagation of the pentagonal order. It is called an "ideal" (defect-free) model for the considered structure.
In Arlington County, The Pentagon Memorial was completed and opened to the public on the seventh anniversary of the attacks in 2008. It consists of a landscaped park with 184 benches facing the Pentagon. When the Pentagon was repaired in 2001–2002, a private chapel and indoor memorial were included, located at the spot where Flight 77 crashed into the building.
The main difficulty in solving the puzzle is overcoming the functional fixedness of putting the pentagon piece either horizontally or vertically; and related to this, the tendency of trying to fill up the notch of the pentagon. In one study participants were found to spend over 60% of their attempts on such misguided placements of the pentagon piece. And even when the pentagon piece happened to be placed properly, it was mostly not recognized as part of the solution, as a match with the T is not easily seen. The puzzle is easily solved when the insight is reached that the pentagon is part of both the horizontal and vertical stem of the T and that the notch in the pentagon constitutes an inside corner.
Although the Department of Defense was not shut down, the February 4, 2019 date for release of the Pentagon's 2020 budget was delayed by at least one month. This had repercussions on the interim period which is usually used by Pentagon planners for adjustments before the 2020 fiscal year which will begin in October 2019. The White House Office of Management and Budget, which oversees the Pentagon request, was shut down when the Pentagon budget arrived in December, and remained inactive, so no work was done on the budget.
After that, Pentagon Jr. defeated Sami Callihan in a Mask vs. Hair match, when Pentagon performed a package piledriver to win the match. After the match, Pentagon shaved Callihan's hair with a razor on the ramp, while Fenix held Callihan's arms.
In 1958 and 1959, most of the obstacles to the construction of Federal Office Building 5 were removed. Congress enacted legislation in 1958 authorizing the construction of the museum on the north side of Independence Avenue between 4th and 7th Streets SW. In 1959, when Congress passed legislation authorizing the construction of GSA's "Little Pentagon" project, removing the distance limitation. Funds for the construction were appropriated in 1960. The exact location of the structure was still unclear, but GSA wanted it built on Independence Avenue. The construction of such a large complex was not considered to be a problem. Congress and GSA believed that a large building helped to create a "dramatic northern boundary" for the redevelopment area. There was still some doubt as to which tenants would occupy the "Little Pentagon". There was some indication that Federal Office Building 10 would house the "Little Pentagon". But in January 1961, GSA allocated Federal Office Building 10 to the Federal Aviation Administration and said it would build the "Little Pentagon" elsewhere in Southwest.
The Pentagon road network is a system of highways, mostly freeways, built by the United States federal government in the early 1940s to serve the Pentagon in northern Virginia. The roads, transferred to the Commonwealth of Virginia in 1964, are now state highways. The main part of the network is the "Mixing Bowl" at Interstate 395 (Shirley Highway) and Route 27 (Washington Boulevard), named because it had major weaving issues with traffic "mixing" between the two roads before it was rebuilt in the early 1970s.
Fort Madalena, which is located at the eastern extremity of the line, was second of the forts to be built. It was built on the site of a fifteenth century chapel dedicated to Mary Magdalene, which gave the fort its name. Construction of the pentagonal fort began in 1878 and was completed in 1880, at a total cost of £9400. The fort itself is quite small, with the short sides of the pentagon being about 30 metres long. The entire fort is surrounded by a 6-metre deep and 4-metre wide ditch. It was armed with a single RML 11-inch gun, four 64-pounders, two 40-pounders and two field guns. Later on, an artillery battery was built around the pentagonal fort, facing the sea for coastal defence. The battery was armed with two BL 9.2-inch guns.
Both borders enclose a continuous region of the plane whose points map to unique equilateral pentagons. Points outside the region just map to repeated pentagons—that is, pentagons that when rotated or reflected can match others already described. Pentagons that map exactly onto those borders have a line of symmetry.
The Pentagon Shopping Centre (known locally as 'The Pentagon') is a shopping centre in Chatham in Kent. The shopping centre is located next to the Waterfront bus station which replaces the Pentagon bus station, which 80% of services use. The shopping centre contains over 70 shops and 7 leisure facilities, many high street names in fashion, homeware and food stores. There are also cafes, restaurants and a bowling alley. As is common with some other 1970's era town centre shopping centres, The Pentagon does not feature a food court or any dedicated dining area. Instead, there are various food outlets scattered throughout the centre. Built as part of the redevelopment of Chatham town centre in the 1970s, the Pentagon also features the high rise Mountbatten House office block, which has controversially stood empty or part-used for most of its history. The Pentagon, Mountbatten House and the Brook multi-storey carpark are built in a distinctive orange-red brick with grey concrete.
The "regular" pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles. It is one of the Johnson solids ("J"). Its height "H", from the midpoint of the pentagonal face to the apex, (as a function of "a", where "a" is the side length), can be computed as:
Its surface area, "A", can be computed as the area of pentagonal base plus five times the area of one triangle:
Its volume when an edge length is known can be figured out with this formula:
The NMCC was begun in early 1962 (opened early October) when the JCS area with the Joint War Room was expanded from ~ to ~ by 1965 (the Pentagon's "Navy Flag Plot" coordinated the Cuban Missile Crisis blockade.) The NMCC was initially considered an "interim" location until the Deep Underground Command Center (DUCC) could be completed below the Pentagon (never built). In December 1963 "SAC accepted the first 465L elements and began to send a limited flow of [data] traffic through them." The NMCC had "direct communications with MACV headquarters in Saigon" during the Vietnam War.
Nadler remarked that "a mosque in the Pentagon ... hasn't drawn any criticism", despite the Pentagon also being a target of the 9/11 attacks. What is referred to as the "Pentagon mosque" is, more precisely, a non-denominational chapel which was built and dedicated in 2002 in honor of Pentagon employees and passengers of American Airlines Flight 77 who died in the September 11 attack. Daily Muslim prayer sessions are held there weekday afternoons, and weekly Muslim services are led by an imam from a local mosque every Friday, which means the room can be considered a "mussallaah", a sacred space where Muslims "consistently perform their mid-day prayer when they do not have access to a mosque". This Muslim use of the Pentagon facility has drawn no complaints.
Penrose originally discovered the P1 tiling in this way, by decomposing a pentagon into six smaller pentagons (one half of a net of a dodecahedron) and five half-diamonds; he then observed that when he repeated this process the gaps between pentagons could all be filled by stars, diamonds, boats and other pentagons. By iterating this process indefinitely he obtained one of the two P1 tilings with pentagonal symmetry.
SR 110 is a part of the Pentagon road network, a network of freeways and surface roads built concurrent with the construction of the Pentagon in the early 1940s. The state highway received its numerical designation in 1964 when maintenance responsibility was transferred to the Virginia Department of Transportation. SR 110's most significant changes in routing were relocation of the highway in Rosslyn to tie into I-66 in the 1980s and relocation of the freeway at the Pentagon to provide a larger security buffer for the building after the September 11 attacks. The highway is sometimes closed for large events held at or around the Pentagon, including the Marine Corps Marathon.
The National Military Command Center opened at the Pentagon in early October 1962 to replace the Air Force Command Post as the Joint Chiefs' command post. The ANMCC included 473L C equipment, including several IBM computers. It was started in early 1962 when the JCS area with the Joint War Room was expanded from ~ to ~ by 1965 (the Pentagon's "Navy Flag Plot" coordinated the Cuban Missile Crisis blockade.) The NMCC was initially considered an "interim" location until the Deep Underground Command Center (DUCC) could be completed below the Pentagon (never built). The NMCC had "direct communications with MACV headquarters in Saigon" during the Vietnam War.The NMCC at (tbd side of the Pentagon) coordinated responses to the 2001 September 11 attacks (AA Flt 77 struck the west side) and other events. By 2008, the NMCC had the NMCC Alert Center for intelligence fusion in the National Operations and Intelligence Watch Officer Network.
Lieberman, "a hawk on foreign policy, has long been considered a friend of defense contractors, both in Connecticut and across the country." He has been "a powerful proponent for robust Pentagon spending and weapons programs." Michael E. O'Hanlon of the Brookings Institution said of Lieberman: "He is a giant of the Senate, to me just as important on national security as Kennedy was on health or Bradley on finance or Domenici on the deficit." "Lieberman cemented his favorable reputation with defense firms when he advocated for more models of combat systems like the Lockheed Martin-made F-22 fighter and the Boeing-built C-17 air lifter even when Air Force and Pentagon officials argued against them."
Generalized pentagonal numbers are closely related to centered hexagonal numbers. When the array corresponding to a centered hexagonal number is divided between its middle row and an adjacent row, it appears as the sum of two generalized pentagonal numbers, with the larger piece being a pentagonal number proper:
When the Washington Metro's Pentagon station originally opened, access to the Pentagon from the station was gained through a direct underground entrance. An outdoor bus station also existed at the station's street entrance.