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## 12.1 Exploring Solids

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**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**Faces, Edges and Vertices**A Cube has 6 Faces, 12 Edges and 8 Vertices.**Cross section**The cutting of a polyhedron or cone by a plane giving different shapes.**Regular Polyhedron**A regular polyhedron has regular polygons for faces**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?**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