SKU: 62417163485

Shapes, Space, and Symmetry

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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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SKU: 62417163485

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4.8 ★★★★★
Based on 7 reviews
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VanillaPepper
Natrona Heights, US
★★★★★ 5
Indestructible Toys My Dobermans ❤️
Size: Large, Color: Mesh Green
Actually Respect! goDog Is a Lifesaver The variety of size and colors are phenomenal 😇 I have two Dobermans — serious, determined power chewers — and I’ve spent years trying to find toys that survive even a few days. I’ve tried the big brands (Kong, Goughnuts, Jolly Ball, you name it) — and while some toys last a little while, almost everything eventually ends up shredded, de-squeaked, or in pieces. goDog toys are the ONLY plush toys my Dobermans won’t destroy. We own multiple goDog toys now — dragons, dinosaurs, lizards — mostly in the large size (perfect for Dobermans), but even a few medium-sized ones hold up surprisingly well. Here’s what’s amazing: • They love them — actually carry them around, toss them, chew them gently, and squeak them happily. • They do not rip them apart — no matter how much tugging, chewing, or wrestling happens. • Large sizes are best for Dobermans (and other big breeds) — but even mediums survive for calmer play sessions. • No ripped seams, no stuffing everywhere, and no destroyed squeakers after months of use. What makes goDog toys different? The secret is their Chew Guard Technology — • A reinforced, high-strength inner mesh layer under the soft plush • Double-stitched seams • Durable yet flexible material that somehow resists punctures, tears, and brutal shaking The outside stays soft and fun, but the inside is built like armor. It’s NOT a super hard rubber or rough canvas — it still feels like a cuddle toy, but it’s engineered to survive serious chewing. Materials include: • Durable polyester plush • Chew Guard inner lining (high-tensile mesh fabric) • Reinforced stitching • Non-toxic squeakers • Safe for dogs to play with long-term Real Owner Advice: • Always size up if you have a heavy chewer — large sizes are a must for Dobermans or similarly strong breeds. • Medium sizes are fine if you supervise or your dog is more moderate with toys, but the large toys are built tougher overall. Final Thoughts: If you have big dogs, strong jaws, or just tired of wasting money on destroyed toys — goDog toys are a must. No other plush-style toy even comes close. My Dobermans will destroy almost anything… but they treat their goDog toys like treasured companions. No holes, no rips, just happy dogs. Follow me here on Amazon for more honest, dog-tested reviews! Like this review if it helped — I’ll be uploading even more proven tough toys and pet essentials soon!
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on April 29, 2025
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Verified Purchase
BB
Battle Creek, US
★★★★★ 4
Surface Fabric is very durable
Size: Small, Color: Hot Pink
Surface Fabric is very durable, but the squeaker didn't last two months. I have urged the manufacturer to find a strong more durable squeaker for their product. My dogs really enoys it when the speaker works. One of his 3 work. I have just bought two more he likes them so much. He takes it to bed every night to catch it once or twice before sleeping. Also loves to catch it a few times during the day.
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Reviewed in the United States on April 11, 2026
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Verified Purchase
Taraknits
Grantham, US
★★★★★ 5
Best. Toy. Ever. For My Superchewer!
Size: Large, Color: Skinny Green, Size: Large, Color: Skinny Green
Best toy ever! My dog destroys toys. Usually within about 15 minutes, she has de-squeakered and defluffed them. By the second day, she has tug-of-war-ed them to shreds. From the time we got this adorable dragon out of the package, she LOVED it. She set to work. It’s been a week, and while she has dewinged him, he lost his squeaker after a few days, and he looks a bit rough, he’s still in one piece! And, we’ve had HOURS of tug-of-war with minimal rips! She’s obsessed 😍 I ordered two more today. We’ve finally found the perfect toy for my baby!
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Reviewed in the United States on January 18, 2026
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Verified Purchase
SnowshoePete
Port Orchard, US
★★★★★ 5
My 90 lb. Pitbull's All-Time Fave Toy
Size: Large, Color: Coral, Size: Large, Color: Coral
I ordered a plethora of new toys for Bruce to keep him occupied while I am working remotely from home. Poor guy gets so bored while I'm stuck in front of my computer 8+ hours a day. All the other toys are animated, but this one is just a big floppy chewy squeaky toy. Bruce quickly lost interest in all the other chirping, hopping, and twirling toys and fell in love with "Diny". When I opened Diny and gave it to Bruce, he had the elated and surprised look of a 3 yr old at Christmas. And he stayed that happy for hours, and then each time he picked up Diny to play. Diny became his go-to toy over all others (and there are many!). It is well made out of durable fabric, and they did not stuff it full of kapoc (I hate kapoc in dogs toys!). And it is delightfully low-tech. Normally he tears a squeaky toy apart as soon as he can isolate the squeaky mechanism. But cleverly, the squeaky box is loose in the long belly so it moves from one end to the other as the toy is handled. That made it difficult for Bruce to locate it. The toy remained in good condition for 2 weeks of near constant attention by Bruce. But yesterday he zeroed in on the squeaky box and ripped Diny to shreds. I was sad to see Diny go so soon. But boy-howdy was Bruce happy with it. I'm gonna buy another because we liked it so much. And so did I : )
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Reviewed in the United States on May 23, 2024
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Jason W
San Leandro, US
★★★★★ 5
This is one “under the radar” gem!!
Size: Large, Color: Coral
This is one “under the radar” gem!! Very strong internal squeaker and way tougher than it looks. My big 125lb Shepard-Husky mix gave it heck, then made it his new buddy. He’ll occasionally give it the business but on the whole, it’s surprisingly tough and my big boy loves it. Nice price!!
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 10, 2026

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