In Four-Point geometry we have the same types of undefined terms as in Three-Poi

Question

In Four-Point geometry we have the same types of undefined terms as in Three-Point geometry, but the following axioms are used:

A1- There are exactly four points.

A2- Two distinct points belong to one and only one line.

A3- Each line has exactly two points belonging to it.

A regular tetrahedron is a polyhedron with four sides being equilateral triangles (pyramid-shaped). If we define a point to be a vertex of the tetrahedron and a line to be an edge, will the tetrahedron be a model for Four-Point geometry? Why or why not?

Explanation / Answer

Yes. All axioms seem to comply. 4 points = 4 vertices two distinct points belong to one and only one line = two distinct vertices defined one and only one edge each line has exactly two points belonging to it = each edge has exactly two vertices belonging to it

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