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PolyhedronPolyhedron
►3-dimensional analog of a polygon3-dimensional analog of a polygon►Closed surface made up of polygonsClosed surface made up of polygons►Any 2 polygons may have only one Any 2 polygons may have only one
shared edgeshared edge
Face
EdgeVertex
PrismPrism
► Polyhedron with 2 opposite faces that Polyhedron with 2 opposite faces that are identical polygonsare identical polygons
►Faces are called basesFaces are called bases
►Bases are joined by lateral faces Bases are joined by lateral faces If the lateral face is a rectangle it is a If the lateral face is a rectangle it is a right right
prismprism
Examples:Examples:
► 2 hexagons for 2 hexagons for basesbases
► Right Hexagonal Right Hexagonal prismprism
► 2 rectangles for 2 rectangles for basesbases
► Right rectangular Right rectangular prismprism
base
Lateral face
PyramidPyramid
► Base is any regular Base is any regular polygonpolygon
► All sides are All sides are trianglestriangles
Platonic SolidsPlatonic Solids
►All sides are equalAll sides are equal►All angles are the sameAll angles are the same►All faces are identicalAll faces are identical►Same number of polygons meet at Same number of polygons meet at
each vertexeach vertex►Only five solids meet these criteria: Only five solids meet these criteria:
Platonic solidsPlatonic solids
TetrahedronTetrahedron
► Composed of 4 Composed of 4 equilateral trianglesequilateral triangles
► 3 triangles meet at 3 triangles meet at vertexvertex
► Represented fire to Represented fire to the ancient Greeksthe ancient Greeks
Hexahedron (Cube)Hexahedron (Cube)
► Composed of 6 Composed of 6 squaressquares
► 3 squares meet at a 3 squares meet at a vertexvertex
► Represented the Represented the stable earthstable earth
OctahedronOctahedron
► Composed of 8 Composed of 8 equilateral trianglesequilateral triangles
► 4 triangles meet at 4 triangles meet at a vertexa vertex
► Represented airRepresented air
DodecahedronDodecahedron
► Composed of 12 Composed of 12 equilateral equilateral pentagonspentagons
► 3 pentagons meet 3 pentagons meet at a vertexat a vertex
► Represented the 12 Represented the 12 signs of the Zodiacsigns of the Zodiac
IcosahedronIcosahedron
► Composed of 20 Composed of 20 equilateral trianglesequilateral triangles
► 5 triangles meet at 5 triangles meet at a vertexa vertex
► Represented waterRepresented water