Geometry: Part 2
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Transcript of Geometry: Part 2
Geometry: Part 2Geometry: Part 23-D figures3-D figures
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
Geometry in the Real World Geometry in the Real World
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
Models of PolyhedraModels of Polyhedra