Eight Convex Deltahedra

Theorem

There exist exactly $8$ distinct convex deltahedra:

$4$ faces: regular tetrahedron

$6$ faces: triangular bipyramid

$8$ 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): $8$