Why cant i build a platonic solid where 6 equilateral triangles meet at each vertex?

Answer 1

You cannot build a platonic solid with six equilateral triangles meeting at each vertex because the angles of equilateral triangles do not allow for a closed three-dimensional shape at that vertex. Each angle of an equilateral triangle is 60 degrees, and six triangles would sum to 360 degrees, which does not leave room for a vertex in three-dimensional space. In contrast, the only platonic solids possible with equilateral triangles are the tetrahedron (3 triangles per vertex) and the octahedron (4 triangles per vertex).