Scalable Vector Graphics (SVG)
SVG is an XML-based vector graphic format for defining two-dimensional graphics. It's a popular format for WikiMedia files that are used in Wikipedia.
A web browser can display SVG files standalone or from within an HTML IMG tag.
For example:
<img class="tfpPhoto" alt="4-cube" width="160" src="svg/4cubeHLinesDash.svg">
These diagrams are modified versions from Wikipedia samples or created using the SVG editor Inkscape or initially generate with ChatGPT.
SVG 3 and 4 Dimensional Cube Diagrams
| Cube Diagrams | ||
|---|---|---|
| SVG 3-Cubes | ||
| 3D cube, all edges the same | Cube with dashed hidden lines | Cube with hidden lines removed |
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All edge lines and vertices are the
same.
This is similar to the one posted on WikiMedia Commons 3-cube graph which is used in the as a B3 Coxeter plane graph orthographic projection. | Hidden lines and vertices are respectively marked as dashed and lighter. | Hidden lines removed which is the version on the Wikipedia hidden line article. |
| 4-Cube Diagrams | ||
| SVG 4-Cubes | ||
| 4-cube, all edges the same | 4-cube with dashed hidden lines | 4-cube with hidden lines removed |
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|
All edge lines and vertices are the
same.
This is basically the same as the one posted on WikiMedia Commons 4-cube graph which is used in the tesseract article as a B4 Coxeter plane graph orthographic projection. | Hidden lines and vertices are respectively marked as dashed and lighter. | Hidden lines removed which is the version on the Wikipedia hidden line article. |
Chess Game
A colleague offered to play a game of chess, and I took him up on it. This gave me a chance to work on my SVG skills.
| Game board development steps: | |||
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| I had ChatGPT generate chess board. I modified it to meet my requirements. | I downloaded each of the SVG chess pieces from Wikipedia. I added them into a single SVG file. | I added the Wikipedia chess pieces onto the board. |
The chess board and pieces are used in an
online game.
I added a replay option to re-watch the game. I should add more options such as pause and continue. |
Other 4-Cube Diagrams
Dash hidden lines,
no circles at the vertices.
Modified using an SVG editor
Inkscape.
ChatGPT generated SVG image.
It generated a version similar to the WikiMedia Commons
4-cube graph.
ChatGPT wrote, "I created the SVG tesseract as a Coxeter-plane projection
using the Coxeter-element eigenvector
ω=eπi/4
ω=e
πi/4".
ChatGPT image modified to have the hidden lines as dashed lines.
4-cube
on Wikipedia that
similar to my 4-cubes.
Rhombic dodecahedron has the above 4-cube the section: Related polytope. I should add the same for the 5-cube and 6-cube polyhedron Wikipedia articles.
A polytope is the generalization of a polygon to any number of dimensions, meaning it is a geometric object with flat sides. Examples include a 2-dimensional polygon and a 3-dimensional polyhedron, and they can be defined as the intersection of half-spaces.
Graphing with ChatGPT
sGraphXYa 2D graph with unit markers
sGraphXYb 2D graph with unit markers and a square centered around the origin.
sGraphWXYZa ChatGPT 4D graph
sGraphWXYZb ChatGPT 4-cube attempt #1.
sGraphWXYZc ChatGPT 3-cube in a 4D graph. The cube's z cube angle does not match the z axis angle.
sGraphWXYZd ChatGPT 4-cube attempt #2. The 4th dimension of the cube is totally incorrect.
sCube1 drawn with polygons.