Answer to Question #342149 in Geometry for licks

Question

This question combines the concepts platonic solids, prisms, pyramids and polyhedra.

 

a) Are any Platonic solids pyramids? If so, which one(s)? Name the pyramid and explain why it is a pyramid (3).

b) Are any Platonic solids prisms? If so, which one(s)? Name the prism and explain why it is a prism (3). 

c)  All Platonic solids are polyhedral. Is this statement true? Explain why you say so (2).

d) Name a non-polyhedron and say why it cannot be a platonic solid (2).

Answer 1

A) Yes. The main Platonic bodies include the tetrahedron, it can be attributed to the pyramid. Also, the correct pyramid can be attributed to Platonic bodies. For example, the Great Egyptian Pyramids. 

b) Yes. The cube is one of the 5 Platonic solids. The cube can be attributed to a kind of prism. An example of the prism supports of some stone bridges. A three-dimensional body having pairs of parallel equal sides.

c) If we rely on the 5 main Platonic solids, then yes. If we count the polyhedron from the number 4, then of course, yes. In general, there are many varieties of Platonic solids, but one way or another they consist of 5 fundamental ones!  

d) Not polyhedron. For example, a round aquarium or a circus tent, these elements consist of round figures (circle, cylinder). They are cast and not multifaceted, although this is quite a controversial issue and if you dig deep, you can argue endlessly. In general, they are not Platonic because they are not polyhedra.