Polyhedron A polyhedron is simply a three-dimensional solid which consists of a collection of polygons, joined at their edges. A polyhedron is said to be regular if its faces and vertex figures are regular polygons.

Platonic Solids

What do these polyhedra have in common?

Name that figure. . . Rectangular Prism Triangular Prism Hexagonal Prism Heptagonal Prism

What do these polyhedra have in common?

Name that figure. . . Rectangular Pyramid Triangular Pyramid Pentagonal Pyramid Hexagonal Pyramid

Prisms vs. Pyramids Two congruent, parallel faces are the bases Sides are parallelograms Named by its base One base Sides are triangles Named by its base http://www.math.com/school/subject3/lessons/S3U4L1GL.html

Polyhedra Faces: Polygonals regions that make up the surface of a solid Edges: The line segments created by the intersection of two faces of a solid Vertices: The points of intersection of two or more edges

Figure Number of Faces Number of Vertices Number of Edges Counting Parts of Solids, Navigations (Geometry), Grades 3-5 Figure Number of Faces Number of Vertices Number of Edges Rectangular Prism (Cube) Pentagonal Prism Rectangular Pyramid Pentagonal Pyramid

Figure Number of Faces Number of Vertices Number of Edges 6 8 12 Counting Parts of Solids, Navigations (Geometry), Grades 3-5 Figure Number of Faces Number of Vertices Number of Edges Rectangular Prism (Cube) 6 8 12 Pentagonal Prism Rectangular Pyramid Pentagonal Pyramid

Figure Number of Faces Number of Vertices Number of Edges 6 8 12 7 10 Counting Parts of Solids, Navigations (Geometry), Grades 3-5 Figure Number of Faces Number of Vertices Number of Edges Rectangular Prism (Cube) 6 8 12 Pentagonal Prism 7 10 15 Rectangular Pyramid Pentagonal Pyramid

Figure Number of Faces Number of Vertices Number of Edges 6 8 12 7 10 Counting Parts of Solids, Navigations (Geometry), Grades 3-5 Figure Number of Faces Number of Vertices Number of Edges Rectangular Prism (Cube) 6 8 12 Pentagonal Prism 7 10 15 Rectangular Pyramid 5 Pentagonal Pyramid

Figure Number of Faces Number of Vertices Number of Edges 6 8 12 7 10 Counting Parts of Solids, Navigations (Geometry), Grades 3-5 Figure Number of Faces Number of Vertices Number of Edges Rectangular Prism (Cube) 6 8 12 Pentagonal Prism 7 10 15 Rectangular Pyramid 5 Pentagonal Pyramid

12 8 6 12 8 9 6 15 10 18 12 5 8 5 6 6 10 6 7 12 7 Explain the relationship that exists among the number of faces, edges, and vertices of each solid in the chart. Faces + vertices = edges + 2 F + v = e + 2

F + v = e + 2 A polyhedron has 7 faces and 15 edges. How many vertices does it have?

F + v = e + 2 A polyhedron has 10 edges and 6 vertices. How many faces does it have?

F + v = e + 2 A polyhedron has 6 faces and 8 vertices. How many edges does it have?

Geometry July 1, 2008

Connect Math Shapes Set http://phcatalog.pearson.com/component.cfm?site_id=6&discipline_id=806&subarea_id=1316&program_id=23245&product_id=3502 CMP Cuisenaire® Connected Math Shapes Set (1 set of 206) ISBN-10: 157232368X ISBN-13: 9781572323681 Price: $29.35

Surface Area 10 inches 3 inches 5 inches

Surface Area 6 inches 4 inches 3 inches 2 inches 5 inches 5 inches

Surface Area 2 in 4’ 2 in 2 in 4’ 4’

Pentominos How many ways can you arrange five tiles with at least one edge touching another edge? Use your tiles to determine arrangements and cut out each from graph paper.

Pentominos http://www.ericharshbarger.org/pentominoes/

Which nets will form a box without a lid?

Building a Box Illuminations: How many different nets can you draw that can be folded into a cube? http://illuminations.nctm.org/activitydetail.aspx?ID=84

It’s the view that counts! (3-5 Geometry, Navigations) When you have a 3-D shape, what do you see when you look at eye level from the front, then from above, and then at eye level from the side? How could you represent the shape so that someone else might be able to build it?

It’s the view that counts! (3-5 Geometry, Navigations) Using three linking blocks, draw on grid paper a two-dimensional representation of the front, side, and top views of your building. Label the views.

It’s the view that counts! (3-5 Geometry, Navigations) FRONT SIDE TOP

It’s the view that counts! (3-5 Geometry, Navigations) Using four linking blocks, draw on grid paper a two-dimensional representation of the front, side, and top views of your building. Label the views. Have your neighbor recreate your building based on your views.

It’s the view that counts! (3-5 Geometry, Navigations)

It’s the view that counts! (3-5 Geometry, Navigations) Transfer your drawing to a three-dimensional view.

Isometric Explorations (6-8 Geometry, Navigations)

Isometric Explorations (6-8 Geometry, Navigations)

Isometric Explorations (6-8 Geometry, Navigations)

Isometric Explorations (6-8 Geometry, Navigations)

Volume Cylinder vs. Cone Cube vs. Square pyramid

Archimedes’ Puzzle 1 8 2 4 9 3 10 12 13 7 6 11 5 14

http://mabbott.org/CMPUnitOrganizers.htm