Edges, vertices, and faces
Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces
What a learner can do afterwards
- Count the edges, vertices, and faces of common 3-D shapes
- Use the terms edge, vertex (vertices), and face correctly
- Describe a 3-D shape by its properties (e.g. a cube has 6 faces, 12 edges, 8 vertices)
1 · Read
A face is a flat part of a solid's surface. Curved parts are not faces here. On a cube, an edge is a straight line where two faces meet. A vertex is a corner where straight edges meet. We call more than one vertex vertices.
A cube has 6 square faces, 12 edges and 8 vertices. Count edges in groups: 4 around the top, 4 around the bottom and 4 joining them. Count vertices: 4 on top and 4 underneath. Each edge belongs to two faces. Counting all 4 sides of every face counts each edge twice.
Count each part once, including parts hidden in a picture. Turning a solid does not change its counts. Compare the same kind of part on both solids. A cuboid has 6 rectangular faces: top and bottom, front and back, left and right. To find unchecked faces, count on from the checked number to 6.
A triangular prism looks like a tent. It has 2 triangle faces and 3 rectangle faces, so 5 faces in all. Each triangle end has 3 edges. Three more edges join the ends, making 9 edges. Each end has 3 vertices, making 6 vertices altogether.
A square pyramid has one square base and 4 triangle faces. Count the base too: it has 5 faces. Its base has 4 edges. Four more edges go from the base corners to the top point, making 8 edges. It has 4 base vertices and one top vertex, making 5 vertices.
Faces are flat, edges are the lines where faces meet, and vertices are the corners. Count each part just once.
Lesson, practice questions and flashcards written for this dataset.
Readings and practice questions written for this dataset. Video links compiled for this dataset. Linked videos by Khan Academy and Math with Mr. J.
More to read
Flat faces and curved parts
Look at a closed box and a tin can. The box has flat faces. The can's two flat circle ends are faces too. The part between those ends curves. We call it a curved part of the surface, not a face. A sphere curves all the way around and has no flat faces. Use the same face rule whenever you count.
Count the whole solid
A drawing may hide part of a solid. Count the whole solid, including the parts behind the front faces. For a cube's vertices, count four on top and four underneath. For a triangular prism's vertices, count three at each triangle end. Turning either solid changes your view, but its vertices stay part of the same solid.
Two faces can share an edge
Find the line where a cube's top face meets its front face. That is one edge shared by two faces. Counting it while checking the top and again while checking the front counts it twice. Try a different plan: count four edges around the top, four around the bottom and four joining top to bottom. These groups count all twelve edges once.
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2 · Watch
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