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Solids and nets

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Cube, cuboid, prism, pyramid, cylinder, cone and sphere: you get to know the most important solids. Then a cube is unfolded and folded again.
📄 Open worksheet (PDF, German)

The video

In the video a cube is unfolded into a net. Then nets are folded into cubes.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:20 Faces, edges, vertices
  3. 1:26 The solids
  4. 2:04 The cube net
  5. 2:42 Careful, mistake!
  6. 3:02 Try it yourself

The most important points

Faces, edges, vertices

A solid (der Körper) is bounded by faces (die Flächen). Edges (die Kanten) are where two faces meet. Vertices (die Ecken) are where three edges meet. The cube has 6 faces, 12 edges and 8 vertices.

The cube: 6 faces, 12 edges, 8 vertices. Invisible edges are dashed.
The cube: 6 faces, 12 edges, 8 vertices. Invisible edges are dashed.

Cube, cuboid, prism and pyramid have only flat faces. Cylinder, cone and sphere have a curved (gewölbt) face.

Cylinder, cone and sphere.
Cylinder, cone and sphere.

The cube net

When you unfold a solid, you get a net (das Netz). A cube net (das Würfelnetz) has 6 squares of the same size. There are 11 cube nets. But not every set of 6 squares makes a cube!

A cube net is folded into a cube.
A cube net is folded into a cube.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

How many faces, edges and vertices does a cuboid have? And a triangular prism?

Show solution

Cuboid: 6 faces, 12 edges, 8 vertices. Triangular prism: 5 faces, 9 edges, 6 vertices.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Körper (Würfel, Quader, Prisma, Pyramide, Zylinder, Kegel, Kugel), Flächen, Kanten und Ecken, Würfelnetze. Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.