Defns. for 3-dimensional figuresDefns. for 3-dimensional figures• Polyhedron – a solid bounded by polygonsthat enclose a single region of shape. (nocurved parts & no openings!)• Faces – the polygons (or flat surfaces)• Edges – segments formed by theintersection of 2 faces• Vertex – point where three or more edgesintersect
Faces, Edges and VerticesThree dimensional (3D) shapes are defined by the number of faces,edges and vertices (corners) that they have.VERTEX(plural is vertices)EDGETETRAHEDRONFACE
ExEx: Is the figure a polyhedron? If so, howmany faces, edges, & vertices are there?Yes,F =V =E =569No, thereare curvedparts!Yes,F =V =E =7712
Types of Solids• Prism – 2 ≅ faces (called bases) in planes. i.e. first example• Pyramid – has 1 base, all other edgesconnect at the same vertex. i.e. lastexample• Cone – like a pyramid, but base is a circle.• Cylinder – 2 circle bases.or• Sphere – like a ball.
More definitions• Regular polyhedron – all faces are ≅,regular polygons. i.e. a cube• Convex polyhedron – all the polyhedrawe’ve seen so far are convex.• Concave polyhedron –“caves in”• Cross section – the intersection of a planeslicing through a solid. Good picture onp.720
5 regular polyhedra• Also called platonic solids.• Turn to page 721 for good pictures at the topof the page.• Tetrahedron – 4 equilateral Δ faces• Cube (hexahedron) – 6 square faces• Octahedron – 8 equilateral Δ faces• Dodecahedron – 12 pentagon faces• Icosahedron – 20 equilateral Δ faces
ExEx: How many faces, edges, & vertices arethere?F =V =E =569F =V =E =7712F + V = E + 25 + 6 = 9 + 211 = 11F + V = E + 214 = 14