8 November 2018

Apeirogon

noun

– a polygon with infinite sides.

Origin

(from the Greek word ἄπειρος apeiros, “infinite, boundless” and γωνία gonia, “angle”)

Example

A regular apeirogon has equal edge lengths, just like any regular polygon, {p}. Its Schläfli symbol is {∞}, and its Coxeter–Dynkin diagram is CDel node 1.pngCDel infin.pngCDel node.png. It is the first in the dimensional family of regular hypercubic honeycombs. An isogonal apeirogon has a single type of vertex and alternates two types of edges. A quasiregular apeirogon is an isogonal apeirogon with equal edge lengths. An isotoxal apeirogon, being the dual of an isogonal one, has one type of edge, and two types of vertices, and is therefore geometrically identical to the regular apeirogon. It can be shown seen by drawing vertices in alternate colors. All of these will have half the symmetry (double the fundamental domain sizes) of the regular apeirogon. Apeirogons in the hyperbolic plane, most notably the regular apeirogon, {∞}, can have a curvature just like finite polygons of the Euclidean plane, with the vertices circumscribed by horocycles or hypercycles rather than circles. Regular apeirogons that are scaled to converge at infinity have the symbol {∞} and exist on horocycles, while more generally they can exist on hypercycles.

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On this day

8 November 1836 – birth of Milton Bradley, U.S. board-game maker, credited with launching the board-game industry. Died 30 May 1911.

8 November 1847 – birth of Bram Stoker, Irish novellist, author of ‘Dracula’. Died 20 April 1912.

8 November 1960 – 43 year old, John F. Kennedy wins the presidential election and becomes the youngest President of the United States of America.

8 November 1973 – In Brisbane, Australia, a home-made bomb is placed on a teacher’s desk. It detonates, killing one student, injuring 8 others, while the teacher loses both hands.