1. 9.5: Symmetry
By the end of class you will be able to list line and rotational symmetries of two and three-dimensional objects
A STUDY IN SOLID GEOMETRY Polyhedra 1

2. Lines of Symmetry Must be a _________________for an object.
These are the Five Platonic Solids   Now, each of the solids have planes or flat surfaces.  These flat surfaces are called faces but I do not like to word face as others apply it.  I like the word surface better because when I think of the word face I picture that an object has a front and a back with the front being the face.  When you rotate or turn a flat surface on a polyhedra perpendicular to your nose, that becomes its new "face" therfore its new front.   So, I make a feeble effort to try to eliminate this confusion by using the word surface.  Even though I use the words point, apex, and vertex redundantly here, actually a point on a geometric solid is called a vertex for the singular and vertices for the plural.

3. Rotational Symmetry.
When an object is mapped onto itself by a rotation between 0 and 360 degrees about the center of the figure (known as the center of symmetry/point of symmetry)
TETRAHEDRON: The word "Tetra" is a Greek word and it has something to do with the number "four."  Now, with a tetrahedron you have an equileteral triangle as its base.  Then you place an equilateral triangle at each edge of the base then they all come up to a point, apex, or vertex if you will.  So, with "tetra" meaning "four",  you have four surfaces.  The tetrahedron was also associated somehow with "Fire" in Plato's day.
These are the Five Platonic Solids.
Now, each of the solids have planes or flat surfaces. These flat surfaces are
called faces but I do not like to word face as others apply it. I like the word
surface better because when I think of the word face I picture that an object has a front and a back with the front being the face. When you rotate or turn a flat surface on a polyhedra perpendicular to your nose, that becomes its new "face" therfore its new front. So, I make a feeble effort to try to eliminate this confusion by using the word surface. Even though I use the words point, apex, and vertex redundantly here, actually a point on a geometric solid is called a vertex for the singular and vertices for the plural.

4. What uppercase letters of the alphabet have rotational symmetry?4

5. Plane Symmetry
When a three dimensional object can be mapped onto itself by a reflection in a ___________.
HEXAHEDRON: This is your standard cube, but "Hex" comes from the Greek meaning "six."  About the only fascinating thing about this solid is that when you rotate it to where a point, apex, or vertex is perpendicular to your nose, you should notice that the outer edges form a "hexagon."  And, this solid was associated with the "Earth" for some reason. Now, when this solid is constructed as a frame, without welding or solder, it is very unstable.  The "Earth" is a very unstable thing because of its volcanoes and earthquakes.
TETRAHEDRON:
The word "Tetra" is a Greek word and it has something to do with the number "four." Now, with a tetrahedron you have an equileteral triangle as its base. Then you place an equilateral triangle at each edge of the base then they all come up to a point, apex, or vertex if you will. So, with "tetra" meaning "four", you have four surfaces. The tetrahedron was also associated somehow with "Fire" in Plato's day.

6. Plane Symmetry

7. How many planes of symmetry does a cube have????7

8. How many planes of symmetry does a pyramid have?8

9. Axis Symmetry
When a three dimensional figure can be mapped onto itself by a rotation between 0 and 360 degrees by a line.
OCTOHEDRON: "Octo" means "eight" in the Greek.  I describe this solid as if you would take two pryamids and glue the basses squarely together, therefore creating "eight" surfaces if you will.  Now, the fascinating thing about this solid is that when you rotate or turn a point, apex, or vertex perpendicular to your nose you are looking at a "top" of a pryamid.  And, in Plato's day this was associated with "Air" somehow!
HEXAHEDRON:
This is your standard cube, but "Hex" comes from the Greek meaning "six" so this solid has six surfaces. About the only fascinating thing about this solid is that when you rotate it to where a point, apex, or vertex is perpendicular to your nose, you should notice that the outer edges form a hexagon. And, this solid was associated with the "Earth" for some reason. Now, when this solid is constructed as a frame, without welding or solder, it is very unstable. The "Earth" is a very unstable thing because of its volcanoes and earthquakes.

10. Summarizer: Name 1 thing…
Summarizer: Name 1 thing…. 1) You already knew about symmetry 2) You learned about symmetry
Q? and A. Well, any?
ICOSAHEDRON:
"Icosa" comes from the Greek and it has something to do with the number twenty somehow. This solid is constructed of twenty equalateral triangles in a ball shape and it was associated with "Water" somehow.