1. 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.

2. Platonic Solids

3. What do these polyhedra have in common?

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

5. What do these polyhedra have in common?

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14.
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

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

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

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

18. Geometry July 1, 2008

19. Connect Math Shapes Set
CMP Cuisenaire® Connected Math Shapes Set (1 set of 206) ISBN-10: X ISBN-13: Price: $29.35

21. Surface Area
10 inches
3 inches
5 inches

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

23. Surface Area
2 in 4’
2 in
2 in 4’ 4’

24. 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.

25. Pentominos

26. Which nets will form a box without a lid?

27. Building a Box Illuminations:
How many different nets can you draw that can be folded into a cube?

28. 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?

29. 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.

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

31. 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.

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

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

34. Isometric Explorations (6-8 Geometry, Navigations)

35. Isometric Explorations (6-8 Geometry, Navigations)

36. Isometric Explorations (6-8 Geometry, Navigations)

37. Isometric Explorations (6-8 Geometry, Navigations)

39. Volume
Cylinder vs Cone
Cube vs Square pyramid

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