Characteristics of Regular 4-Dimensional Polytopes
Theorem
The $4$-dimensional regular polytopes have the following characteristics:
| Name | No. of cells | No. of faces | No. of edges | No. of vertices | Dual |
|---|---|---|---|---|---|
| Pentatope | $5$ | $10$ | $10$ | $5$ | Self-dual |
| Tesseract | $8$ | $24$ | $32$ | $16$ | $16$-cell |
| $16$-cell | $16$ | $32$ | $24$ | $8$ | Tesseract |
| $24$-cell | $24$ | $96$ | $96$ | $24$ | Self-dual |
| $120$-cell | $120$ | $720$ | $1200$ | $600$ | $600$-cell |
| $600$-cell | $600$ | $1200$ | $720$ | $120$ | $120$-cell |
Proof
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$