Year 10 Advanced Mathematics

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Year 10 Advanced Mathematics

• Convex
• Regular
• Solids

More correctly known as
PLATONIC SOLIDS
or
?
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What are Platonic solids? ?
Lets quickly revise solids in general
Solids can be broken up into 2 groups ?
Prisms
and
Pyramids
Then the names depend on the ...
number of faces
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Q. What does it mean to be a Platonic solid? ?
A. Each of the faces must have the same length
sides AND...
All the faces in the solid must be the same.
Q. Which ones satisfy our 2 criteria so far?? ?
In the prisms, the only one that does is the..
And in the pyramids, the only one that does is
the..
There must be more!
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Q. Why are they the first two Regular solids??
A. The first shape for each face of any Regular
solid must have 3 sides and the next shape must
have 4 sides on each of its faces.
Q. What are the special names that are used for
each of these solids?
Triangular Pyramid
A. The one with 3 sides is called a ?
and the one with 4 sides is called a ?
Cube
Both of them have other names
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Both these names come from the Greek
language. Hedron means surfaces the prefixes
say how many.
What other polygons could our regular solids have
as their faces?
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All solids are made up of flat surfaces which
meet at both their edges and their vertices.
Q. How many faces MUST at least meet at each
vertex?
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Look at the solids you have made
Some questions to help you decide the other
regular solids
How many regular polygons can meet at each vertex?
Which regular polygons will not make a solid?
What part of each of the polygons tells you
whether it will work to make a regular solid or
not?
Now, .
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Cut out the diagrams on the second sheet to be
able to answer these questions. Put them
together with the cut-out from the person next to
you.
The answers to our questions for the other
regular solids were
How many regular polygons can meet at each vertex?
3 or 4
Which regular polygons will not make a regular
solid?
All polygons with more than 5 sides
What part of each of the polygons tells you
whether it will work to make a regular solid or
not?
The angles.
The last answer gives us another question
What must the sum of the angles of the polygons
at any vertex be less than?
360
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So, which regular shapes will work to make
regular convex vertex points? ?
and
Pentagons
Triangles
Squares
When you used 3 equilateral triangles meeting at
a vertex, you had the start of a ?
Tetrahedron
When you used 4 equilateral triangles meeting at
a vertex, you had the start of an ?
Octahedron
When you used 5 equilateral triangles meeting at
a vertex, you had the start of an ?
Icosahedron
These are the only convex regular polyhedra with
equilateral triangles as their faces. ?
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What about Squares and Pentagons? ?
It was only possible to use 3 squares meeting at
a vertex. You had the start of a ?
Hexahedron (cube)
With the Pentagons, your diagram from the
investigation sheet only had 3 of them, giving a
total at any vertex of 3 ? 108 324. It was
the start of a
Dodecahedron
It was impossible to use 3 hexagons because each
has an angle of 120, already giving a total of
360
These are the only other convex regular polyhedra
with regular shapes as their faces.
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So, there are 5 Platonic Solids.
They are the
Cut out the other nets for the other 3 Platonic
solids andcomplete the table on the worksheet