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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 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.

GeoB 11.4 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.

GeoB 11.4 Platonic Solids Chart 3


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

 

Vertices
GeoB 11.4 Euler Formula GeoB 11.4 Platonic Solids Chart 4 GeoB 11.4 Platonic Solids Chart2
Nets of Platonic Solids
  • Click any of these “nets” of the 5 Platonic solids to download and print your own!

Dodecahedron

GeoB 11.4 DodecahedronHexahedron (Cube)

GeoB 11.4 Hexahedron

Icosahedron
GeoB 11.4 Icosahedron OctahedronGeoB 11.4 OctahedronTetrahedronGeoB 11.4 Tetrahedron

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.

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