The tetrahedron has 3 triangles connecting at each vertex, resulting in 4 total triangles, while the octahedron has 4 triangles connecting at each vertex (8 total triangles), and the icosahedron ...

Look for arcs inside each vertex. The same number of arcs indicate equal angles. Different numbers of arcs indicate different angles. To identify the symmetry of a triangle: Count how many ways ...

It's actually better to work it out for each vertex, rather than for each individual triangle, but given that there will always be more of the former, compared to the latter, it's quicker just to ...