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28-579: Four Oaks may refer to the following places: Four Oaks, East Sussex , an area in England Four Oaks, Gloucestershire , an area in England Four Oaks, Kent , an area in England Four Oaks, Solihull , West Midlands, England, a settlement in Berkswell parish Four Oaks, Sutton Coldfield , West Midlands, an area in England Four Oaks, Kentucky , United States Four Oaks, North Carolina ,

56-636: A number of octagonal churches in Norway . The central space in the Aachen Cathedral , the Carolingian Palatine Chapel , has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral . Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, such as in

84-416: A number of hamlets and settlements as well as Berkswell village. These include Beechwood , Carol Green , and Four Oaks , as well as the eastern part of Balsall Common . Berkswell railway station serves the village, but is actually much closer to Balsall Common than to Berkswell village (it was formerly 'Berkswell & Balsall Common' station). The Church of England parish church of St. John Baptist

112-415: A regular octagon is 135 ° ( 3 π 4 {\displaystyle \scriptstyle {\frac {3\pi }{4}}} radians ). The central angle is 45° ( π 4 {\displaystyle \scriptstyle {\frac {\pi }{4}}} radians). The area of a regular octagon of side length a is given by In terms of the circumradius R , the area is In terms of

140-480: A right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of eight isosceles triangles, leading to the result: for an octagon of side a . The coordinates for the vertices of a regular octagon centered at the origin and with side length 2 are: Coxeter states that every zonogon (a 2 m -gon whose opposite sides are parallel and of equal length) can be dissected into m ( m -1)/2 parallelograms. In particular this

168-571: A town in North Carolina, United States [REDACTED] Topics referred to by the same term This disambiguation page lists articles about distinct geographical locations with the same name. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Four_Oaks&oldid=1224287296 " Category : Place name disambiguation pages Hidden categories: Short description

196-491: Is r16 and no symmetry is labeled a1 . The most common high symmetry octagons are p8 , an isogonal octagon constructed by four mirrors can alternate long and short edges, and d8 , an isotoxal octagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular octagon. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only

224-408: Is a hexadecagon , {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be a truncated square. The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then

252-479: Is a late-12th century Norman building, notable for its two-part crypt . The eastern part is a rectangular space of two bays under the chancel . The western part is an unusual octagonal space under the eastern part of the nave . Later features of the church include the Perpendicular Gothic windows of the north aisle and the two-storied wooden porch. Berkswell's toponym is derived from

280-600: Is a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D 4d , [2 ,8] symmetry, order 16. The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes , shown in these skew orthogonal projections of in A 7 , B 4 , and D 5 Coxeter planes . The regular octagon has Dih 8 symmetry, order 16. There are three dihedral subgroups: Dih 4 , Dih 2 , and Dih 1 , and four cyclic subgroups : Z 8 , Z 4 , Z 2 , and Z 1 ,

308-560: Is different from Wikidata All article disambiguation pages All disambiguation pages Berkswell Berkswell ( / ˈ b ɜːr k s w əl / BURK -swəl ) is a village and civil parish in the Metropolitan Borough of Solihull , county of West Midlands , England. Historically in Warwickshire , Berkswell is situated in the rural east of the borough, approximately 2 miles (3.2 km) west of

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336-421: Is the protected and restored Berkswell Windmill , a fine example of a tower mill with its original machinery. Other local features include Marsh Lane Nature Reserve. There is a small Church of England primary school near the church on Church Lane. Notable people from Berkswell include the actor Jeremy Brett , whose roles include Sherlock Holmes in a television drama series, tennis player Maud Watson –

364-450: Is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular octagon , m =4, and it can be divided into 6 rhombs, with one example shown below. This decomposition can be seen as 6 of 24 faces in a Petrie polygon projection plane of the tesseract . The list (sequence A006245 in the OEIS ) defines the number of solutions as eight, by

392-419: The apothem r (see also inscribed figure ), the area is These last two coefficients bracket the value of pi , the area of the unit circle . The area can also be expressed as where S is the span of the octagon, or the second-shortest diagonal; and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of

420-750: The g8 subgroup has no degrees of freedom but can be seen as directed edges . The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa , Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery , Zum Friedefürsten Church (Germany) and

448-499: The Berks Well, a 16 ft (5 m) square, stone-walled water well just outside the churchyard . It is said to have been used for baptisms by immersion and can still be seen today. There are several 16th and 17th century houses in the village. The Bear Inn dates from the 16th century. The local history society runs a small museum in a 17th-century cottage near the church. Ram Hall, about 0.5 miles (800 m) southeast of

476-596: The Birmingham League, winning the league's Twenty20 Cup competition in 2010. Numerous television series have shot scenes in Berkswell – including BBC's Beat the Boss and ITV's Comedy/Drama Love and Marriage . Octagon A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square , t{4}, which alternates two types of edges. A truncated octagon, t{8}

504-509: The eight orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings . A skew octagon is a skew polygon with eight vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes. A regular skew octagon is vertex-transitive with equal edge lengths. In three dimensions it

532-426: The eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles ) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base. Given the length of a side a , the span S is The span, then, is equal to the silver ratio times the side, a. The area is then as above: Expressed in terms of

560-529: The first Ladies Singles Champion in 1884 at The Championships, Wimbledon and Bob Wyatt (R.E.S.), England Cricket Captain for a number of years from 1934. The Beastie Boys stayed in the village for two weeks in 1988, writing the B-side Jubbsy's Treasure . Former county cricketer Dominic Ostler , a key member of Warwickshire's historic treble winning side in 1994, who lives in neighbouring Balsall Common , went on to skipper Berkswell Cricket Club in

588-404: The formulas for their length: A regular octagon at a given circumcircle may be constructed as follows: A regular octagon can be constructed using a straightedge and a compass , as 8 = 2 , a power of two : The regular octagon can be constructed with meccano bars. Twelve bars of size 4, three bars of size 5 and two bars of size 6 are required. Each side of a regular octagon subtends half

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616-402: The last implying no symmetry. On the regular octagon, there are eleven distinct symmetries. John Conway labels full symmetry as r16 . The dihedral symmetries are divided depending on whether they pass through vertices ( d for diagonal) or edges ( p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the regular form

644-415: The midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other). The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on

672-412: The regular octagon in terms of the side length a is and the inradius is (that is one-half the silver ratio times the side, a , or one-half the span, S ) The inradius can be calculated from the circumradius as The regular octagon, in terms of the side length a , has three different types of diagonals : The formula for each of them follows from the basic principles of geometry. Here are

700-506: The sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square. A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of

728-519: The span, the area is Another simple formula for the area is More often the span S is known, and the length of the sides, a , is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths e on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being e = a / 2 , {\displaystyle e=a/{\sqrt {2}},} may be calculated as The circumradius of

756-525: The village, was built about 1600. The Old Rectory, now called The Well House, south of the church, is early 18th century, then replacing a rectory whose records go back to early 17th century. The almshouses were built in 1853. There is a village green on which are the stocks that were used for punishing petty offenders. It is claimed that these were especially built for a one-legged ex-soldier and his two drinking companions as there are only five leg holes. On Windmill Lane in neighbouring Balsall Common

784-423: The western city boundary of Coventry , at Eastern Green . It is situated about 6.5 miles (10.5 km) west of Coventry city centre, 8.5 miles (13.7 km) east of central Solihull , 2.5 miles (4.0 km) south of Meriden and 2 miles (3.2 km) north of Balsall Common . The United Kingdom Census 2001 recorded a parish population of 2,843, increasing to 3,139 at the 2011 Census. The parish includes

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