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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 20sided 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 threedimensional 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 onedimensional objects. 
Two points make a segment. 
Congruent onedimensional 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.

 Ex 3. Cones and cylinders are NOT polyhedrons.

Important!
Practice (Apex Study 11.4)
 Try practice problems on Pg 13
 Mandatory: write and answer problems on Pg 14
 1 Quiz
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