Green Academy Geometry

Geometer’s Sketchpad Activity 16: Platonic Solids

Adapted from The Geometer’s Sketchpad 101 Project Ideas1

A two-dimensional template for folding a three-dimensional solid is called a net. Use Geometer’s Sketchpad to construct nets for each of the five platonic solids, complete with folding tabs. (A net for each platonic solid is shown on subsequent pages). Then print out your nets and build the solids.

Tetrahedron

1. Use Geometer’s Sketchpad to construct a tetrahedron net complete with tabs. Use the example on page 4 of this document as a guide.

Hint: You will find it beneficial to use the Rotation and Midpoint functions of Sketchpad.

Q1: Multiple Choice. What is the relationship between the Tetrahedron net you were given in this document and the Tetrahedron net on Sketchpad. (Note: ignore the net’s tabs when answering this question)

A) They are similar. B) They are congruent.

Q2: Prove your answer to question 1.

2. Print out your net, decorate it, cut it out and build your solid.

Cube

3. Use Geometer’s Sketchpad to construct a cube net complete with tabs. Use the example on page 5 of this document as a guide.

Hint: You will find it beneficial to use the Rotation, Mark Vector and Translate functions of Sketchpad.

Q3: Multiple Choice. What is the relationship between the Cube net you were given in this document and the Cube net you created on Sketchpad.

A) They are similar. B) They are congruent.

Q4: Prove your answer to question 3. (Note: ignore the net’s tabs when answering this question)

4. Print out your net, decorate it, cut it out and build your solid.

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas2

Dodecahedron

5. Use Geometer’s Sketchpad to construct a dodecahedron net complete with tabs. Use the example on page 6 of this document as a guide.

Hint: You will find it beneficial to use the Rotation function of Sketchpad.

Q5: Multiple Choice. What is the relationship between the dodecahedron net you were given in this document and the dodecahedron net you created on Sketchpad.

A) They are similar. B) They are congruent.

Q6: Prove your answer to question 5. (Note: ignore the net’s tabs when answering this question)

6. Print out your net, decorate it, cut it out and build your solid.

Octahedron

7. Use Geometer’s Sketchpad to construct an octahedron net complete with tabs. Use the example on page 7 of this document as a guide.

Hint: You will find it beneficial to use the Rotation function of Sketchpad.

Q7: Multiple Choice. What is the relationship between the octahedron net you were given in this document and the octahedron net you created on Sketchpad.

A) They are similar. B) They are congruent.

Q8: Prove your answer to question 7. (Note: ignore the net’s tabs when answering this question)

8. Print out your net, decorate it, cut it out and build your solid.

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas3

Icosahedron

9. Use Geometer’s Sketchpad to construct an icosahedron net complete with tabs. Use the example on page 8 of this document as a guide.

Hint: You will find it beneficial to use the Rotation, Mark Vector, and Translate functions of Sketchpad.

Q9: Multiple Choice. What is the relationship between the icosahedron net you were given in this document and the icosahedron net you created on Sketchpad.

A) They are similar. B) They are congruent.

Q10: Prove your answer to question 9. (Note: ignore the net’s tabs when answering this question)

10. Print out your net, decorate it, cut it out and build your solid.

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas4

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas5

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas6

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas7

Green Academy Geometry

Adapted from The Geometer’s Sketchpad 101 Project Ideas8