Polyhedra in Poland

By Pawlikowski, Piotr | Mathematics Teaching, September 2007 | Go to article overview

Polyhedra in Poland

Pawlikowski, Piotr, Mathematics Teaching

Piotr Pawlikowski gives a personal account of his relationship with polyhedra.

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for me 3-D geometry is the branch of mathematics that shows the beauty of tangible physical forms - as well as the beauty of mathematical reasoning.

My personal adventure with polyhedra began in 1996 during an annual conference of SNM (Polish Mathematics Teachers' Association). Until then, despite being a mathematics graduate and a professionally active teacher, my knowledge about polyhedra did not go beyond the above-mentioned stereotypes. During the conference, I met Jan Baranowski and saw his collection of polyhedra and 3-D puzzles. For the first time, I saw physical models of Archimedean solids and I learned about the existence of the Kepler-Poinsot solids. When I got home, I tried to make some simple models of polyhedra. The first attempts were rather ineffective, but in the course of time I became so skilled that building models turned into something more than just a hobby. The book which allowed me to take my first steps was Mathematical Models (Cundy and Rollett, 1981). In a short time, I had built all the polyhedra presented in that book. I also developed my interest by joining an SNM working group 'Warsztat Otwarty' (Open Workshop), where I met a lot of great people who inducted me into the land of polyhedra! My small collection of polyhedra gradually grew into Archimedean solids, Kepler-Poinsot solids, stellations of an icosahedron, compounds of Platonic polyhedra and many others.

At the beginning of 2002, in a local museum in my hometown, Kluczbork, I presented an exhibition of my collection. During three weeks, over 3300 people visited the museum to see the exhibition. In autumn of the same year, a similar number of people (but over the course of only three days) saw my models at the Lower Silesian Science Festival in Wroclaw. Along with my models of uniform polyhedra, there were also polyhedra models made by my students. They prepared a complete set of 92 regular-faced convex polyhedra (called Johnson's solids). …

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Polyhedra in Poland
Settings

Settings

Typeface
Text size Reset View mode
Search within

Look up

Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
• Highlights & Notes
• Citations
Some of your highlights are legacy items.

How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.