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Description
Shapes, Space, and Symmetry"Altogether a most instructive, entertaining, and esthetically pleasing book." Science. Since the ancient Greeks, the visualization of space has been a challenge that has intrigued men of learning. Through centuries of thoughtful looking, a number of three dimensional figures or polyhedral, as the Greeks called them, have been discovered, admired, and wondered at for their mathematical elegance and beauty. And they have been put to use in remarkably
"Altogether a most instructive, entertaining, and esthetically pleasing book." -- Science.Since the ancient Greeks, the visualization of space has been a challenge that has intrigued men of learning. Through centuries of thoughtful looking, a number of three-dimensional figures or polyhedral, as the Greeks called them, have been discovered, admired, and wondered at for their mathematical elegance and beauty. And they have been put to use in remarkably diverse ways by engineers and builders, chemists and crystallographers, architects and sculptors.
This book describes very clearly and simply, and illustrates with beautiful photographs of models, a great number of three-dimensional figures, all but a few consisting of plane faces bounded by straight lines. It examines the nine regular solids -- the five commonly called Platonic, described by Theaetetus in the fourth century B.C., and the four called Kepler-Poinsot, two each of which were discovered by Kepler and Poinsot many centuries later. And it examines many variations obtained by truncation, stellation, dualization, and compounding.
Writing for the layman as well as the student or professional in mathematics, Alan Holden explains the structure of the figures and demonstrates how they can be used to explain mathematics visually rather than by symbol systems, an effort hailed by Scientific American magazine as "a victory of clear, connected thinking over the theorematic method." At the end of the book the author includes a section containing instructions for constructing cardboard models.
Binding Type: Paperback
Publisher: Dover Publications
Published: 03/14/2012
ISBN: 9780486268514
Pages: 208
Weight: 0.65lbs
Size: 8.90h x 5.90w x 0.60d
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4.1 ★★★★★
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Product Reviews
★★★★★ 1
Stopped working within 3 days
Color: Blue
Worked for 3 plays. My 11 week old puppy loved this item. Unfortunately, it only lasted 3 tries before the motor stopped working. $30 for a total of 30 minutes over 3 days is robbery! I'd look at another vendor for the same type of item. We charged it after each attempt but now the motor won't turn on.
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Reviewed in the United States on February 12, 2026
★★★★★ 3
Item was returned
Color: Blue
Used it one day and partially the following day. Put on charger. Never worked again. My dog played with it but returned it as defective.
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Reviewed in the United States on April 12, 2026
★★★★★ 4
Not for super chewers
Color: Blue
This ball seems to be of good quality; has held a charge well and is easy to use. Sadly, the cover lasted less than 15 minutes with our dog.... not for aggressive chewers for sure. Pretty funny to watch the hound dog jowls shake though.
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Reviewed in the United States on January 25, 2026
★★★★★ 5
Great fun for dogs!
Color: Orange
Two of our dogs really love this! It caused a lot of barking and chasing and running around trying to grab it. It's really funny to use the remote to control it (and especially make it stop when things get a little too chaotic!) It feels durable even when pawed and bumped into and stepped on. The battery life seems good. I plugged it in overnight to charge so not sure how long it took to charge, but it has lasted quite a while with the dogs playing with it and still doesn't need a charge. It's easy to screw off one side of the ball to plug it in to charge. The size is a little bigger than a tennis ball I would say and has a soft texture.
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Reviewed in the United States on January 6, 2026
★★★★★ 1
It doesn't work.
Color: Blue
The two halves of the ball shell come apart again and again when the dog plays with them. When it is time to recharge the core, it will not take a charge. The dog loves it, but it's unsafe to play with.
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Reviewed in the United States on January 15, 2026