How many convex solids have the same faces?

geometry 3d solid-geometry

Convex polyhedra with regular faces which are not Platonic are called Johnson solids. There are 5 Johnson solids with the same faces. It happens they are all triangular faced (can you see why?)

  • J12 Triangular bipyramid
  • J13 Pentagonal bipyramid
  • J17 Gyroelongated square bipyramid
  • J51 Triaugmented triangular prism
  • J84 Snub disphenoid

So together with 5 Platonic solids, you have 10.

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