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Net to Solid Explorer

Run the Net to Solid Explorer MicroSim Fullscreen
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About This MicroSim

A net is a flat pattern that folds into a solid. The left panel shows the net with every face labeled and colored, and the fold lines dashed. The right panel shows the same net folding as you move the slider, from completely flat at 0% to a closed solid at 100%.

Click any face in the net and it is outlined in red in both panels, so you can follow one face from the flat pattern to its place on the solid.

The strip below counts the faces, edges, and vertices of the finished solid and checks Euler's formula, \(V - E + F = 2\), which is true for every solid in this MicroSim.

How to Use

  1. Choose a solid from the Solid menu.
  2. Drag Fold slowly from 0% to 100% and watch each face turn about its dashed fold line.
  3. Click a face of the net to highlight it on the folding solid. Click it again to clear the highlight.
  4. Turn on Auto-rotate and keep the pointer over the MicroSim to view the solid from all sides.
  5. Check the counts of faces, edges, and vertices against the closed solid.

Iframe Embed Code

<iframe src="main.html"
        height="532"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9-12 (High School Geometry)

Duration

10-15 minutes

Prerequisites

Names of prisms and pyramids, and the terms face, edge, and vertex.

Bloom's Taxonomy Level

Understand (L2)

Learning Objective

Students will be able to explain how a two-dimensional net folds into a three-dimensional solid and identify which face of the net becomes which face of the solid.

Activities

  1. Predict (4 min): With the fold at 0%, students predict which face of the cube net will end up opposite the base, then fold to check.
  2. Trace (5 min): Students click each face of the square pyramid net in turn and describe the path it takes as the slider moves.
  3. Count (5 min): Students count faces, edges, and vertices on each closed solid, compare with the display, and verify Euler's formula.

Assessment

Students are given three patterns of six squares and decide which fold into a cube, justifying each decision by naming the faces that would overlap or leave a gap.

References

  1. Wikipedia. Net (polyhedron).
  2. Wikipedia. Euler characteristic.
  3. Common Core State Standards Initiative. Grade 6 Geometry (6.G.A.4) and High School Geometry: Geometric Measurement and Dimension (HSG-GMD.B.4).