+26388 What is e=nf/2?
The Platonic Solids:
Euler's formula:
V - E + F = 2.
the number of vertices(V), minus the number of edges(E), plus the number of faces(F), is equal to two.
see e=nf/2 in : Proof of five Platonic solids in link:
http://www.physics.miami.edu/huerta/class/mls603/Platonic_Solids_proof.pdf;3
+26388 What is e=nf/2?
The Platonic Solids:
Euler's formula:
V - E + F = 2.
the number of vertices(V), minus the number of edges(E), plus the number of faces(F), is equal to two.
see e=nf/2 in : Proof of five Platonic solids in link:
http://www.physics.miami.edu/huerta/class/mls603/Platonic_Solids_proof.pdf;3
+118654 Thanks Heureka,
Do these need to be regular solids?
I am assuming that it will work for irregular ones as well but does it work for shapes such as stars where some of the intenal angles are acute ??
I've seen this formula a number of times before but I have never had cause to use it. ://
+26388 Hello Melody,
...Euler's formula is true for every polyhedron.
The only polyhedra for which it doesn't work are those that have holes running through them like the one shown in the figure below...
...It involves the Platonic Solids, a well-known class of polyhedra named after the ancient Greek philosopher Plato, in whose writings they first appeared....
see: https://plus.maths.org/content/eulers-polyhedron-formula
