# 11.4 – Platonic Solids

## Key Terms

• Dodecahedron – A Platonic solid made from 12 congruent regular pentagons.
• Hexahedron – A Platonic solid with six faces.
• Icosahedron – A 20-sided solid in which each side is a polygon.
• Each side of a regular icosahedron is an equilateral triangle.
• Octahedron – A Platonic solid made from eight congruent equilateral triangles.
• Platonic Solids – A group of five special polyhedrons made of congruent regular polygonal faces with the same number of faces meeting at every vertex.
• Tetrahedron – A Platonic solid made from four congruent equilateral triangles.

## Review

Polyhedron
• A three-dimensional solid bounded by polygons

## Notes

History
• The Platonic solids are named after the ancient Greek philosopher Plato.
• Plato considered math a branch of knowledge connected with the highest level of thought.
• Five very special polyhedrons were once considered the building blocks of the universe: the platonic solids.

Platonic Solids
• Properties
• Five special polyhedrons
• All faces are congruent
• All faces are regular polygons
• Same number of faces meet at each vertex
• Three polygon faces that make all Platonic solids
• Equilateral triangles
• Squares
• Regular pentagons
Building a Platonic Solid
• Just as regular polygons can be constructed from a repeating line segment, Platonic solids can be constructed from a repeating regular polygon.
• Platonic solids can be constructed from the repetitive folding of polygons.
Step Example
Points form one-dimensional objects. Two points make a segment.
Congruent one-dimensional objects form regular polygons. Four congruent segments make a square.
Congruent regular polygons form Platonic solids. Six congruent squares make a hexahedron.

• Prefixes
• Tetra means 4
• Hexa means 6
• Octa means 8
• Dodeca means 12
• Icosa means 20

Vertices
Nets of Platonic Solids
• Click any of these “nets” of the 5 Platonic solids to download and print your own!

Dodecahedron

Hexahedron (Cube)

Icosahedron
OctahedronTetrahedron

## Examples

 Ex 1. Not all prisms or pyramids are Platonic solids. The only Platonic solid that is a pyramid is a Tetrahedron. Ex 2. One Platonic solids is also a cube. It is a hexahedron. Ex 3.  Cones and cylinders are NOT polyhedrons.