Octagon facts for kids
In geometry, an octagon is an eight-sided polygon.
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} is a hexadecagon, t{16}.
Contents
Properties of the general octagon
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 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 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.
Uses of octagons
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 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, notably the Intelsat Headquarters in Washington D.C., Callam Offices in Canberra, and Octagon Offices in Parramatta, Australia.
Other uses
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Umbrellas often have an octagonal outline.
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The famous Bukhara rug design incorporates an octagonal "elephant's foot" motif.
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Janggi uses octagonal pieces.
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Japanese lottery machines often have octagonal shape.
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Stop sign used in English-speaking countries, as well as in most European countries
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An icon of a stop sign with a hand at the middle.
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The trigrams of the Taoist bagua are often arranged octagonally
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Famous octagonal gold cup from the Belitung shipwreck
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Classes at Shimer College are traditionally held around octagonal tables
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The Labyrinth of the Reims Cathedral with a quasi-octagonal shape.
Related pages
Images for kids
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A regular skew octagon seen as edges of a square antiprism, symmetry D4d, [2+,8], (2*4), order 16.
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The movement of the analog stick(s) of the Nintendo 64 controller, the GameCube controller, the Wii Nunchuk and the Classic Controller is restricted by a rotated octagonal area, allowing the stick to move in only eight different directions.
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An octagonal prism contains two octagonal faces.
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An octagonal antiprism contains two octagonal faces.
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The truncated cuboctahedron contains 6 octagonal faces.
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The omnitruncated cubic honeycomb
See also
In Spanish: Octógono para niños
