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.

PolyhedronPolyhedron

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 SolidsPlatonic Solids

What do these polyhedra have in What do these polyhedra have in common?common?

Name that figure. . .Name that figure. . .

Heptagonal Prism

Triangular Prism

Hexagonal Prism

Rectangular Prism

What do these polyhedra have in What do these polyhedra have in common?common?

Name that figure. . .Name that figure. . .

Hexagonal Pyramid

Triangular Pyramid

Pentagonal Pyramid

Rectangular Pyramid

Prisms vs. PyramidsPrisms vs. Pyramids

Two congruent, Two congruent, parallel faces are the parallel faces are the basesbases

Sides are Sides are parallelogramsparallelograms

Named by its baseNamed by its base

One baseOne base

Sides are trianglesSides are triangles

Named by its baseNamed by its base

http://www.math.com/school/subject3/lessons/S3U4L1GL.html

PolyhedraPolyhedra Faces: Polygonals regions Faces: Polygonals regions

that make up the surface of a that make up the surface of a solidsolid

Edges: The line segments Edges: The line segments created by the intersection of created by the intersection of two faces of a solidtwo faces of a solid

Vertices: The points of Vertices: The points of intersection of two or more intersection of two or more edgesedges

FigureFigure Number of Number of FacesFaces

Number of Number of VerticesVertices

Number of Number of EdgesEdges

Rectangular Rectangular Prism (Cube)Prism (Cube)

Pentagonal Pentagonal PrismPrism

Rectangular Rectangular PyramidPyramid

Pentagonal Pentagonal PyramidPyramid

Counting Parts of Solids, Navigations (Geometry), Grades 3-5





66 88 1212









66 88 1212


77 1010 1515








66 88 1212


77 1010 1515


55 55 88







66 88 1212


77 1010 1515


55 55 88


66 66 1010


6 12 8

6 12 8

5 9 6

7 15 10

8 18 12

5 8 5

4 6 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. A polyhedron has 7 faces and 15 edges. How many vertices does it have?How many vertices does it have?

F + v = e + 2

A polyhedron has 10 edges and 6 vertices. A polyhedron has 10 edges and 6 vertices. How many faces does it have?How many faces does it have?

F + v = e + 2

A polyhedron has 6 faces and 8 vertices. A polyhedron has 6 faces and 8 vertices. How many edges does it have?How many edges does it have?

GeometryGeometryJuly 1, 2008July 1, 2008

Connect Math Shapes SetConnect Math Shapes Set

http://phcatalog.pearson.com/component.cfm?http://phcatalog.pearson.com/component.cfm?site_id=6&discipline_id=806&subarea_id=1316&program_id=23245&prsite_id=6&discipline_id=806&subarea_id=1316&program_id=23245&product_id=3502oduct_id=3502

CMP Cuisenaire® Connected Math CMP Cuisenaire® Connected Math Shapes Set (1 set of 206)Shapes Set (1 set of 206)ISBN-10:ISBN-10: 157232368X 157232368XISBN-13:ISBN-13: 9781572323681 9781572323681Price:Price: $29.35 $29.35

Surface AreaSurface Area

5 inches

3 inches

10 inches


4 inches

6 inches

3 inches

5 in

ches

5 inches

2 inches

5 inches


4’4’

4’4’

4’4’

2 in

2 in

2 in

PentominosPentominos

How many ways can you arrange five tiles How many ways can you arrange five tiles with at least one edge touching another with at least one edge touching another edge? edge?

Use your tiles to determine arrangements Use your tiles to determine arrangements and cut out each from graph paper. and cut out each from graph paper.

PentominosPentominos

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

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

Building a BoxBuilding a Box

Illuminations: Illuminations:

How many different nets can you draw that How many different nets can you draw that can be folded into a cube?can be folded into a cube?

http://illuminations.nctm.org/activitydetail.aspx?ID=84http://illuminations.nctm.org/activitydetail.aspx?ID=84

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

When you have a 3-D shape, what do you When you have a 3-D shape, what do you see when you look at eye level from the see when you look at eye level from the front, then from above, and then at eye front, then from above, and then at eye level from the side?level from the side?

How could you represent the shape so that How could you represent the shape so that someone else might be able to build it?someone else might be able to build it?


Using three linking blocks, draw on grid Using three linking blocks, draw on grid paper a two-dimensional representation of paper a two-dimensional representation of the front, side, and top views of your the front, side, and top views of your building. Label the views. building. Label the views.


FRONT TOPSIDE


Using four linking blocks, draw on grid paper Using four linking blocks, draw on grid paper a two-dimensional representation of the a two-dimensional representation of the front, side, and top views of your building. front, side, and top views of your building. Label the views. Label the views.

Have your neighbor recreate your building based on your views.



Transfer your drawing to a three-Transfer your drawing to a three-dimensional view. dimensional view.

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




VolumeVolume

Cylinder Cylinder vs. vs. Cone Cone

Cube vs. Square pyramidCube vs. Square pyramid

lwhV

BhV

3

13

1

hrV 2 hrV 2

3

1

lwhV

BhV

Archimedes’ PuzzleArchimedes’ Puzzle

1

4

11

3

2

9

8

6 7

5 14

10

12 13

http://mabbott.org/CMPUnitOrganizers.htmhttp://mabbott.org/CMPUnitOrganizers.htm

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.

Documents

edges slide

solid edges

polyhedra faces

solid vertices

parallel faces

navigations geometry

counting parts of solids

platonic solids