<Dd> δ = 2 π − q π (1 − 2 p). (\ displaystyle \ delta = 2 \ pi - q \ pi \ left (1 - (2 \ over p) \ right).) </Dd> <P> By a theorem of Descartes, this is equal to 4π divided by the number of vertices (i.e. the total defect at all vertices is 4π). </P> <P> The 3 - dimensional analog of a plane angle is a solid angle . The solid angle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by </P> <Dl> <Dd> Ω = q θ − (q − 2) π . (\ displaystyle \ Omega = q \ theta - (q - 2) \ pi . \,) </Dd> </Dl>

Where are platonic solids found in real life