Shapes

Platonic Solids are the fundamental building blocks of geometric form in our universe, as well as the most symmetrical of polyhedra. According to Plato, there are five shapes that represent the perfect forms of earth, air, fire, water, and aether. In our reality, these shapes are the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. However, in an alternate reality, the five Platonic Solids may have been defined differently:

1. Tetrahedron: This is a regular polyhedron with four triangular faces and is analogous to the tetrahedron in our reality.
2. Cube: This Platonic Solid is a regular polyhedron with six square faces and is also identical to the cube in our reality.
3. Icosahedron: A regular polyhedron with 20 triangular faces, similar to the icosahedron in our reality.
4. Dodecahedron: A regular polyhedron with 12 pentagonal faces, which is also consistent with its representation in our universe.
5. Hexahedroid: A non-convex regular polyhedron formed by 24 congruent equilateral triangles in this alternate reality. It is a more complex shape than the Octahedron found in our reality, which is composed of just eight equilateral triangles.

The differences between the Platonic Solids in this alternate reality and our own can have significant implications for many areas of mathematics, science, art, and philosophy. In this reality, the Hexahedroid may be used in architecture, as well as in the creation of crystalline structures found in nature. It could also be at the core of aesthetic and philosophical discussions about the nature of form and dimensionality.