Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

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}.

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.

Octagonal (disambiguation)

Octagonal refers to the property of being like an octagon.

Octagonal may also refer to:

Octagonal (horse)

Octagonal (foaled 8 October 1992) is a retired champion New Zealand-bred, Australian raced Thoroughbred racehorse, also known as 'The Big O' or 'Occy'. He was by the champion sire Zabeel, out of the champion broodmare Eight Carat, who also produced Group One winners Mouawad, Kaapstad, Diamond Lover and (Our) Marquise.

Trained by John Hawkes, Octagonal made his debut late in 1994, and was crowned the Australian Champion Two Year Old on the strength of his autumn campaign, which comprised wins in the Todman Trial and AJC Sires Produce Stakes and close seconds in the STC Golden Slipper and AJC Champagne Stakes.

As a three-year-old, Octagonal won seven of his eleven starts, and took his record to 10 wins from 16 starts. In addition to beating a high-standard crop in Sydney's three-year-old autumn triple crown - the Canterbury and Rosehill Guineas and the Australian Derby - Octagonal won the two richest weight-for-age races on the Australian calendar, the W S Cox Plate and the Mercedes Classic. With earnings of just short of A$4 million, Octagonal was voted the 1996 Australian Champion Three Year Old, Australian Horse of the Year, and remains the last horse to have won the triple crown. The Victoria (spring) and Australian Derby (autumn) double eluded him, however, as he was narrowly defeated by Nothin' Leica Dane in the Victoria Derby.