Display Title
3D Geometry Animation: Cube
Display Title
3D Geometry Animation: Cube
VIDEO: 3D Geometry Animation: Cube
Learn about the Platonic Solids by watching this video. (The transcript is also included.)
Video Transcript
IN ANCIENT GREECE THE PHILOSOPHER PLATO
DESCRIBED A SET OF THREE DIMENSIONAL SHAPES
THAT HAVE SINCE COME TO BEAR HIS NAME:
THE PLATONIC SOLIDS.
LET'S START WITH THEIR TWO DIMENSIONAL
COUNTERPARTS
AND BUILD THEIR THREE DIMENSIONAL VERSION.
LOOK AT THIS EQUILATERAL TRIANGLE.
IT IS A REGULAR POLYGON
WHERE ALL SIDES AND ANGLE MEASURES ARE CONGRUENT.
THIS TWO DIMENSIONAL NET WHEN FOLDED THIS WAY
BECOMES THE THREE DIMENSIONAL SOLID
CALLED A TETRAHEDRON,
WHICH IS ONE OF THE PLATONIC SOLIDS.
BECAUSE OF THE UNDERLYING REGULAR POLYGON,
THE TETRAHEDRON HAS CONGRUENT EDGES,
VERTICES AND ANGLES.
NOW LOOK AT THIS SQUARE,
WHICH IS A REGULAR QUADRILATERAL.
WE USE THAT SQUARE TO CONSTRUCT
A TWO DIMENSIONAL NET.
WE FOLD THIS NET TO CONSTRUCT A CUBE,
WHICH IS ANOTHER PLATONIC SOLID
ALSO REFERRED TO AS A HEXAHEDRON.
THE "HEX" IN HEXAHEDRON REFERS TO SIX,
WHICH IS THE NUMBER OF SIDES IN A CUBE.
LIKE THE TETRAHEDRON
THE EDGES, VERTICES AND ANGLES OF THE CUBE
ARE CONGRUENT TO EACH OTHER.
THE OTHER PLATONIC SOLIDS INCLUDE THE
EIGHT-FACED OCTAHEDRON...
THE TWELVE-FACED DODECAHEDRON...
AND THE TWENTY-FACED ICOSAHEDRON.
WITH ALL THESE FIGURES,
THE UNDERLYING REGULAR POLYGON SHAPE
ENSURES CONGRUENT EDGES, ANGLES AND VERTICES.
BEYOND THE PLATONIC SOLIDS
ARE MANY DIFFERENT THREE DIMENSIONAL SHAPES.
IN THIS PROGRAM YOU WILL EXPLORE THE PROPERTIES
OF THREE DIMENSIONAL FIGURES.
UNDERSTANDING THE PROPERTIES OF THESE FIGURES
HELPS US UNDERSTAND CERTAIN NATURAL AND
MAN-MADE STRUCTURES THAT SHARE THESE PROPERTIES.
IN PARTICULAR, THIS PROGRAM WILL COVER THE FOLLOWING KEY CONCEPTS:
Properties of 3D Figures
Three-dimensional figures have certain properties that can be analyzed and categorized.
This is a cube.
The surface of the cube is made up of six faces.
A cube has twelve edges.
A cube has eight vertices, also referred to as corners.
Different three-dimensional figures have different numbers of faces, edges, and vertices. Here is a square pyramid.
It has 4 faces, 8 edges, and 5 vertices.
Here is an octahedron, which is like two square pyramids attached a the base.
It has 8 faces, 12 edges, and 6 vertices.
This table summarizes these properties for a number of different three-dimensional shapes.
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Using Nets to Understand 3D Figures
What Is a Net?
A net is a two-dimensional version of a three-dimensional figure. A printed net can be used to build the 3D model. Here are some examples of nets.
This is the net for a cube. Since each face of the cube is a square, the net for a cube consists of a series of squares that fold into a cube.
This is the net for a triangular prism. Notice how the two triangular faces and the rectangular faces connect. This net will fold into a triangular prism.
This is the net for a square pyramid. Notice how the square base connects with the four triangular bases. This net will fold into a pyramid.
Even circular figures can be modeled with a net. Here is the net for a cylinder. Notice how the circular the circular sides of the cylinder align with the rectangular side.
This animated sequence shows a cube from top to bottom.
Note: The download is an MP4 video file.
Related Resources
To see additional resources on this topic, click on the Related Resources tab.
Video Library
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| Common Core Standards | CCSS.MATH.CONTENT.6.G.A.2, CCSS.MATH.CONTENT.7.G.B.6, CCSS.MATH.CONTENT.8.G.C.9, CCSS.MATH.CONTENT.5.MD.C.3.A, CCSS.MATH.CONTENT.5.MD.C.3.B, CCSS.MATH.CONTENT.6.G.A.4, CCSS.MATH.CONTENT.7.G.A.3, CCSS.MATH.CONTENT.HSG.GMD.A.1, CCSS.MATH.CONTENT.HSG.GMD.A.2, CCSS.MATH.CONTENT.HSG.GMD.A.3, CCSS.MATH.CONTENT.HSG.GMD.B.4 |
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| Duration | 0.50 minutes |
| Grade Range | 5 - 10 |
| Curriculum Nodes |
Geometry • 3D Geometry • 3-Dimensional Figures • Cubes |
| Copyright Year | 2012 |
| Keywords | geometry animation |