Determining the number of edges on a spherical polyhedron given edge length and minimum inner diameter

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This came from a silly hypothetical question. How many Seans would it take to contain the Earth inside a Spherical Polyhedron made of 3-Sean triangles*.

I think I have enough information to solve it:

  • Our edge length is 1.98 meters (Sean is 6' 6" tall)
  • Our minimum diameter is 12742000 meters (equatorial earth diameter)

But I'm not sure how to go about solving it.

*Not triangles technically, but you know what I mean

EDIT: Here's what I'm thinking...

  1. Surface area of the earth is ~510000000000000 m^2
  2. Area of Sean-Triangle (1.98m Equilateral) is 1.7m^2
  3. Therefore ~300000000000000 Sean-Triangles

To use Euler's Polyhedron formula I would need to know the number of vertices, and then I could determine the number of edges.