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Platonic Solids
Plato
Profile: Plato (c.427-347 B.C.E.) was born to an aristocratic family in Athens. As a young
man Plato had political ambitions, but he became disillusioned by the political leadership in
Athens. He eventually became a disciple of Socrates, accepting his basic philosophy and
dialectical style of debate, the pursuit of truth through questions, answers, and additional
questions. Plato witnessed the death of Socrates at the hands of the Athenian democracy in
399 BC. In Raphael's School of Athens we see Socrates prone, with cup nearby.
Plato's most prominent student was Aristotle, shown here with Plato in Raphael's School of
Athens, Aristotle holiding his Ethics and Plato with his Timaeus.
Plato's Academy
In 387 BCE Plato founded an Academy in Athens, often described as the first university. It
provided a comprehensive curriculum, including astronomy, biology, mathematics, political
theory, and philosophy.
Plato's final years were spent lecturing at his Academy and writing. He died at about the
age of 80 in Athens in 348 or 347.
Over the doors to his academy were the words
meaning, "Let no one destitute of geometry enter my doors."
1. Find 4 words in the paragraph above that you do not know the meanings of. Underline
the words in the paragraph above.
2. Find the meanings of those words.
3. Find a picture of Plato and Aristotle. Save these to your Z - drive.
4. Find 3 facts about each not given in any part of this paper.
5. What does the word destitute mean and how does it relate to the sign above?
6. What did Plato think of art? Why?
The Platonic Solids
The Platonic Solids belong to the group of geometric figures called polyhedra.
A polyhedron is a solid bounded by plane polygons. The polygons are called faces; they
intersect in edges, the points where three or more edges intersect are called vertices.
A regular polyhedron is one whose faces are identical regular polygons. Only five regular
solids are possible:
cube tetrahedron octahedron icosahedron dodecahedron
These have come to be known as the Platonic Solids.
The solids are named after the ancient Greek philosopher Plato who equated
them with the four classical elements:
earth with the cube,
air with the octahedron,
water with the icosahedron,
and fire with the tetrahedron.
The fifth solid, the dodecahedron, was believed to be used to make the heavens
7. What are plane polygons?
8. What are polyhedrons?
9. Find an example of each of the following:
(Save them in your Z drive.)
a. polygon face
b. edge
c. vertices
d. regular polygons
e. plane polygons
10. Make sure you can describe each of the terms in question #9 as well.
11. Find a picture of each of the Platonic Solids and save each one to your Z drive.
12. Fill in the table below.
Platonic Solid
cube
tetrahedron
octahedron
icosahedron
dodecahedron
polygon face
# of faces
# of edges
# of vertices
Part Two
Your next task will be to construct each Platonic Solid
with your straws. You will need some sort of string to
hang these up when you are finished.
Guidelines:
 No tape or glue to hold them together.
 No overlapping parts along the edges.
 All constructions will be labeled with information
from the table in #12 and your first and last name.
 All constructions will have a string at least 24
inches long. All constructions are due at the end
of this unit which is April 12.
Part Three
You will make some sort of presentation with your
research. You can choose to use Power Point, Glogster,
Animoto or some other pre-approved form to teach the 12
points from above. We want people to watch our
presentation and be able to tell others about what
Platonic Solids are, who they are named for, a brief
history of this person, the geometry associated with
Platonic Solids, etc.
Your exact guidelines will be available by March 20.