Cube with balanced ternary labels

Autor/Urheber:

Watchduck You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

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https://dewiki.de/b/2304ff

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Wikimedia Commons

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1044 x 1116 Pixel (181807 Bytes)

Beschreibung:

The 3³ = 27 face centers of the cube around the unit sphere

The coordinates are assigned to the points based on the usual right-handed coordinate system.
They are then interpreted as balanced ternary numbers from −13 to 13.
The least significant trit is on the left (little-endian), so the enumeration is consistent across dimensions.
(The l.s.t. always corresponds to the first dimension — usually called x.)

In the table on the right the gray boxes to the right of the triples indicate the Hamming weight of each number ( A005812).
The weight (number of non-zero entries) corresponds to what kind of point the coordinate describes:

0	1	2	3
origin	face center (line vertex)	edge center (square vertex)	cube vertex

While the figures (−1, 0, 1) are written as (−, 0, +), the sign of the integers is only expressed by their color.

The positive octant of this cube is the unit cube. Its vertices have the numbers 0, 1, 3, 4, 9, 10, 12, 13 ( A005836).

This SVG was created with Inkscape.

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CC BY-SA 4.0

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