Eight Convex Deltahedra
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Theorem
There exist exactly $8$ distinct convex deltahedra:
- $4$ faces: regular tetrahedron
- $8$ faces: regular octahedron
- $10$ faces: pentagonal bipyramid
- $12$ faces: snub disphenoid (split a regular tetrahedron into two wedges and join them with a band of $8$ equilateral triangles)
- $14$ faces: triaugmented triangular prism (attach $3$ square pyramids to a triangular prism)
- $16$ faces: gyroelongated square bipyramid (attach $2$ square pyramids to a square antiprism)
- $20$ faces: regular icosahedron.
Proof
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$