# Regular Polytela and Other One Dimensional Shapes

This page will deal with regular polytela, 1-D dice, and any other interesting 1-D shapes - or in other words - the dyad. Last updated June 10, 2012.
2012 June 10 - Released online.

2012 April 6 - Polytela page created.

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## Basic One Dimensional Shapes

This shape can be considered as the basic 1-D shape. It is:

**Dyad** - also known as a line segment. It can also be called the ditelon, for it has two endpoints as its sides, which are its vertices. It could be represented by **|**.

## Regular Polytela

A polytelon is a one dimensional polytope. It is regular when all of its vertices are congruent. A uniform polytelon is considered to be a regular polytelon. There are a surprizing number of these - one!, it is convex, orientable, and tame - there are no star versions. Below is a seemingly endless listing of the one and only regular polytelon.

**Dyad** - (DI ad), AKA Ditelon. Behold the magnificence of this polytope, the utter complexity - a shape that strikes terror into anyone who attempts to build one. With a whopping two vertices which are its facets, and its body is its only "edge". It is the shape of the sides of all polygons and the shape of the edges of all uniform polytopes beyond. Its symbol is x and it has two pieces shaped like points which are not connected to each other.

## One Dimensional Dice

A die is any convex shape with congruent "contact regions". Contact regions can be thought of as the part that can contact a surface when the object is setting on one. The one dimensional dice are as follows:

**Dyad** - has 2 sides, its endpoints - it can't be rolled in one dimensional space since rotation is impossible here. Hmmm - where have we seen this one before.

## Other One-Dimensional Shapes

**Ad** - (AD) antiditelon or antidyad. It has two end points, but the center is the hollow part. The infinite part outside the points are the inside of this object.

**Ray** - (RAY) just call him Ray. It has one end point (vertex), one side of it is solid.

Page created by Jonathan Bowers, 2012
e-mail = hedrondude at suddenlink dot net