Tesseract Dimensions: Inner Cube vs Outer Cube

  • Context: High School 
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Discussion Overview

The discussion centers on the dimensions of a tesseract when represented in 3D, specifically the size relationship between the inner cube and the outer cube. Participants explore considerations for visual representation and practical applications such as 3D printing.

Discussion Character

  • Exploratory, Technical explanation, Experimental/applied

Main Points Raised

  • One participant questions the appropriate size of the inner cube relative to the outer cube in a 3D representation of a tesseract.
  • Another participant suggests that the size is arbitrary and can represent different perspectives in 4D, albeit with some simplifications.
  • A participant expresses a practical concern regarding the thickness of the lines connecting the cubes for a 3D printed model.
  • Another reply indicates that the thickness of the lines is based on practical considerations rather than a strict rule.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the size relationship between the inner and outer cubes, and there are differing views on the significance of line thickness in the representation.

Contextual Notes

The discussion does not clarify specific assumptions about the visual representation of tesseracts or the implications of different sizes on understanding 4D geometry.

LightningInAJar
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TL;DR
tesseract dimensions
When drawing a tesseract in 3D how large should the inner cube be compared to the outer one?
 
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It's up to you, it's completely arbitrary. Different sizes will correspond to different points of view in 4D (with some simplifications).
 
I just wanted to 3D print a model. Wasn't sure if the lines leading between the cubes needed a different thickness to be more correct.
 
Well, they are lines, their thickness is purely coming from practical considerations.
 

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