Question

There are 5 paltonic solids. Now the question is, what are the inscribed solids? What shape is contained within each platonic solid with a vertex at the center of each side?

1. Tetrahedron (4) faces made of Triangles

2. Hexahedron (6)Faces made of squares

3. Icosahedron (20) Faces made of Triangles

4. Octahedron (8) Faces made of Triangles

5. Dedecaheron (12) faces made of pentagon shapes

Answer 1

The original discovery of the platonic solids is unknown. The five regular
polyhedra all appear in nature whether in crystals or in living beings. They also
appear all throughout history in children’s toys, dice, art, and in many other
areas. Around 360 B.C. the regular polyhedra are discussed in the dialogues of
Plato, their namesake. The varying solids are likened to each of the elements,
earth, fire, water, and air. He compared the tetrahedron to fire because the sharp
stabbing points and edges reminded Plato of the stabbing heat from flames.
The octahedron was associated with air because its many small smooth parts
makes it seem as though it is barely there. Plato saw the icosahedron as water
because it flows, like water, out of ones hands. And the cube was associated
with earth because its causes dirt to crumble and fall apart, and at the same
time it resembles the solidity of earth. The fifth solid, the dodecahedron, was
considered the shape that encompasses the whole universe and was used for
arranging the constellations in the heavens.