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): $8$
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