Dynamic Construction of Archimedean Solids

Wilfried Dutkowski, GeoGebra Institut NRW, Feb 1, 2026

This book formed the bases to my lecture at the MEDA Conference 2026, which was took place at Johannes Kepler University Linz (JKU) from 15th - 18th of September 2026. It describes the experience of the author when creating dynamic [b]Archimedean solids [/b]and using them in lessons. It also contains some Applets, which are not lesson-proofed, but they demonstrate some difficulties. A German print version is available since August 2026: [url]https://doi.org/10.37626/GA9783959873949.0[/url] An online version is also available. created: [color=#c51414][b]01.02.2026[/b][/color] last edit: [color=#1551b5][b]12.09.2026[/b] [/color] [color=#0a971e][b]published: 18.09.2026[/b][/color] Test lecture: Thursday, 23rd, 2026, University of Cologne, staff-colloquium.

Table of Contents

  1. About the Book
    1. Title
    2. At your disposal
    3. Connected sites
  2. What is a star?
    1. Agenda
    2. Are stars geometric objects?
    3. Extension to 3 dimensions
    4. The famous Herrnhuter Star
  3. Groups of solids
    1. Categorising Polyhedra
  4. Compound Hexahedron Octahedron
    1. How to built? Difficulties
    2. Good to know
    3. Compounding octahedron-hexahedron
  5. Mutual Interpenetration
    1. Another solid?
    2. Mutual Interpenetration
  6. Expanding
    1. Other possibilities?
    2. Rhombicuboctahedron
  7. Bevelling
    1. More solids
    2. Bevelling - tricky but possible
  8. One highlight
    1. Characteristic 0 out of the blue
  9. Conclusion + Discussion
    1. What did we need?
    2. What did we find out?
    3. Some impressions
    4. Discussion
  10. Extension: Non-Convex Solids
    1. Characteristic 1
  11. Lecture at Cologne
    1. Title
    2. What awaits you
    3. Convex solids sorted
    4. Sculptures and personal connection
    5. Facts about solids
    6. Definition and Demarcation
    7. Using spheres
    8. One big difference - geometrically obvious
    9. Using data records
    10. Starting the metamorphosis
    11. Truncating
    12. Union and convex hull
    13. Focus the name
    14. Using duality - extension
    15. Compound octahedron hexahedron
    16. Power of forms
    17. Nerds as solids
    18. Telling the trick
    19. Nerds in action
    20. Icosidodecahedron by mutual interpenetration
    21. Hexahedron - rhombic cuboctaeder by expanding
    22. Expanding + turning = bevelling?
    23. Algebraic background
    24. Symbolic Structure
    25. Metamorphosis of a rhombic cuboctahedron
    26. Why?
    27. Discussion

1.

About the Book

  • 1. Title
  • 2. At your disposal
  • 3. Connected sites

1.1.

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1.2.

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1.3.

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2.

What is a star?

  • 1. Agenda
  • 2. Are stars geometric objects?
  • 3. Extension to 3 dimensions
  • 4. The famous Herrnhuter Star

2.1.

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2.2.

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2.3.

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2.4.

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3.

Groups of solids

  • 1. Categorising Polyhedra

3.1.

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4.

Compound Hexahedron Octahedron

  • 1. How to built? Difficulties
  • 2. Good to know
  • 3. Compounding octahedron-hexahedron

4.1.

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4.2.

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4.3.

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5.

Mutual Interpenetration

  • 1. Another solid?
  • 2. Mutual Interpenetration

5.1.

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5.2.

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6.

Expanding

  • 1. Other possibilities?
  • 2. Rhombicuboctahedron

6.1.

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6.2.

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7.

Bevelling

  • 1. More solids
  • 2. Bevelling - tricky but possible

7.1.

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7.2.

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8.

One highlight

  • 1. Characteristic 0 out of the blue

8.1.

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9.

Conclusion + Discussion

[color=#1551b5][b]Many Thanks to Rudolf Hrach, who printed the 3-D models![/b][/color]

  • 1. What did we need?
  • 2. What did we find out?
  • 3. Some impressions
  • 4. Discussion

9.1.

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9.2.

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9.3.

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9.4.

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10.

Extension: Non-Convex Solids

  • 1. Characteristic 1

10.1.

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11.

Lecture at Cologne

  • 1. Title
  • 2. What awaits you
  • 3. Convex solids sorted
  • 4. Sculptures and personal connection
  • 5. Facts about solids
  • 6. Definition and Demarcation
  • 7. Using spheres
  • 8. One big difference - geometrically obvious
  • 9. Using data records
  • 10. Starting the metamorphosis
  • 11. Truncating
  • 12. Union and convex hull
  • 13. Focus the name
  • 14. Using duality - extension
  • 15. Compound octahedron hexahedron
  • 16. Power of forms
  • 17. Nerds as solids
  • 18. Telling the trick
  • 19. Nerds in action
  • 20. Icosidodecahedron by mutual interpenetration
  • 21. Hexahedron - rhombic cuboctaeder by expanding
  • 22. Expanding + turning = bevelling?
  • 23. Algebraic background
  • 24. Symbolic Structure
  • 25. Metamorphosis of a rhombic cuboctahedron
  • 26. Why?
  • 27. Discussion

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11.6.

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11.7.

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11.8.

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11.9.

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11.10.

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11.11.

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11.12.

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11.13.

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11.14.

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11.15.

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11.16.

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11.17.

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11.18.

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11.19.

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11.20.

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11.21.

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11.22.

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11.23.

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11.24.

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11.25.

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11.26.

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11.27.

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