12.1 Exploring Solids Polyhedron Platonic Solids Cross Section.
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Transcript of 12.1 Exploring Solids Polyhedron Platonic Solids Cross Section.
12.1 Exploring Solids
Polyhedron
Platonic Solids
Cross Section
Definition of a Polyhedron
A polyhedron is a solid formed by many plane faces.
Convex Polyhedron
Convex Polyhedron are polyhedrons where any two points can be connected by a line segment
Convex NonConvex
Faces, Edges and Vertices
A Cube has 6 Faces, 12 Edges
and 8 Vertices.
face edge
vertex
Cross sectionThe cutting of a polyhedron or cone by a
plane giving different shapes.
Regular Polyhedron
A regular polyhedron has regular polygons for faces
Platonic Solids are regular polyhedrons
Can you think of any use of a Icosahedrons?
Euler’s Theorem
The number of faces + number of vertices equals the number of edges plus 2.
Icosahedrons has 20 faces, 12 vertices.
How many
Edges?
Euler’s Theorem
The number of faces + number of vertices equals the number of edges plus 2.
Icosahedrons has 20 faces, 12 vertices.
How many
Edges?
E
E
E
30
232
21220
How many Edges on this shape?
Edge = ½(Shape edges times Number of Shapes + Shape edges times Number of Shapes…..)
How many Edges on this shape?
Edge =
½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)
How many Edges on this shape?
Edge = 68
½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)
How many Vertices on this shape?
Edge = 68, Faces = (6 +10 + 8) = 24
How many Vertices on this shape?
Edge = 68, Faces = (6 +10 + 8) = 24
24 + V = 68 + 2
24 + V = 70
V = 46
Homework
Page 723 – 726
# 10 – 30 even,
32 – 35 , 42- 52,
54, 55