PentaOrbiform mathematically perfect solid of constant width

Rolls like a ball without the smooth edges. The next iteration of Euler's classic Orbiform.
Created by
971 backers pledged \$63,592 to help bring this project to life.

Replay with sound

If you missed out on our Kickstarter, jump on over toAltDynamic.comto get your PentaOrbiforms!

Earlier this year, in our prior Kickstarter campaign, 1,629 awesome backers helped us bring to life a version of an Orbiform based off of a triangle, which was used by Leonardo da Vinci and  Leonhard Euler. With many thousands of Orbiforms in hands around the world, the most common request was "what's the next shape?" It's now here!

Introducing the PentaOrbiform!

Why is it called PentaOrbiform? Because this Orbiform variant is derived from a pentagon and no formal name existed. With polygons of many sides, the terminology "n-gon" is typically used, where "n" is the Greek prefix (tri, tetra, penta, hexa, hepta, octa...). We used this as inspiration for the name PentaOrbiform.

It is a widely accepted axiom that only a circle and a sphere have constant width properties. Generally, nobody gives thought that there might be another shape or group of shapes which have constant width. Unexpectedly, there are other shapes. During the Renaissance, artists and designers, such as da Vinci, began using Orbiforms in their work. However, the shape is so unintuitive, even while drawing and implementing the figure, nobody realized the shape had constant width. Not until the late 18th century while studying optics did Leonhard Euler realize and mathematically prove Orbiforms have constant width. Since then, engineers such as Franz Reuleaux, have used this property to make unique mechanical devices such as square hole cutting drills, man-hole covers, coins, camshafts and rotary engines (Wankel Engine).

We're big fans of excessively designed quality goods, and we're math geeks. The PentaOrbiform is a math-based sculpture which sparks conversation, and lets us pique the curiosity of others who share our passion of math, science and machined goods. Whether you are a designer, engineer, educator, student or math lover, thank you for taking the time to view the campaign!

Math Talk

The PentaOrbiform derived from a pentagon is the close cousin to the triangular Orbiform, which is commonly called a Reuleaux Triangle. Both of these shapes have constant width, however, the PentaOrbiform has slightly more volume for the same height. Also, the perimeter length of a circle, Reuleaux Triangle, and PentaOrbiform can all be calculated with the equation pi*D=circumference.

The 3D PentaOrbiform is the analog to the 2D case, whereby it is rotated on its axis of symmetry to create a convex body of revolution.  A 3D Orbiform can be placed inside a cube of the same width, in any orientation, and simultaneously, tangentially touch all six faces just like a sphere.

Precision Machined

In this campaign, we are using all of the knowledge and experience gained in our prior campaign, where we CNC (computer numerical control) machined thousands of Orbiforms. Our PentaOrbiforms will be CNC machined from solid bars of stainless steel, copper and brass. We will NOT be casting them! Casting would not provide us with the batch consistency, surface finish and quality we want to achieve and also would not be as dimensionally precise as machining.

Our Orbiform and PentaOrbiform will match in dimension (1.4 in) and finish (Machine, Mirror Polish, and Satin).

PentaOrbiform Dimension Specifications:

• Each PentaOrbiform is 1.4 in. (3.55 cm) in width
• Stainless Steel weighs 176 g (6.21 oz.)
• Brass weighs 188 g (6.63 oz.)
• Copper weighs 200 g (7.05 oz.)

Finishes & Metals

PentaOrbiforms are available in stainless steel, copper and brass. You can choose a satin, mirror polish, or machine finish. The pictures below show the nine different options. These pictures are of our prototypes, they are not renderings.

Material Notes: Brass and Copper oxidize when exposed to oxygen in the air, and over time will naturally patina and darken (just like a penny). None of our Orbiforms are coated to slow down patina, and the brass and copper are not plated or painted surfaces, but machined from solid bars of the material. Brass and Copper can easily be cleaned in seconds with a cleaning cream, and can be easily coated to prevent patina. Stainless steel does not patina. Stainless steel is also a much harder metal, and is less easily scratched than copper or brass.

Finishes

Machine Finish: This finish is right off of the lathe. From top to bottom, there is a very fine and consistent texture which in the right conditions will catch the light and reflect some rainbow colors. This finish is the most durable, and is the best at hiding scratches.

Mirror Polish: This finish is highly polished and is literally a small mirror. It is so reflective you can comb your hair in it or see what is happening behind you. It is extremely lustrous.

Satin Finish: This finish has a flat sheen and hides fingerprints well. The surface is dotted with microscopic craters which reflect light in a soft manner. This finish is the same as that found on Apple computers or laptops.

Display Stands

In our prior Kickstarter campaign, we developed our single and triple stands along with our backers. Both sizes are available in carbon fiber and walnut wood. In this campaign, we will try to develop an additional type of stand with our backers. Stands will be available to add-on to your pledge after the campaign ends.

Production Milestone Timeline

We will give regular updates post-campaign to make sure all backers are in the loop! Each blue dot represents a milestone where we will send a campaign update so you are aware of how development is coming along. We will not be like other Kickstarter campaigns that leave their backers in the dark and guessing as to what is happening.

Pledge Rewards

When the campaign ends, you will receive a Kickstarter Backer Survey where you can choose your material options and finish options. We have listed March as to when pledges will be shipped, but are aiming for February. Message us if you have a question on how to pledge.

Notes on Pledges: Our pledge structure is designed to make every combination of material and finish available. Here is an example: If you choose the "3 PentaOrbiforms" reward category, you can choose any combination of metals and you can also choose any combination of finishes for those metals. For instance, a brass-mirror polished, a copper-satin, and a stainless steel-machine finish.

Our Mission is to Make Awesome Products & Happy Backers!

Risks and challenges

All of the prototypes shown are of actual machined PentaOrbiforms (NOT renderings) and units our backers receive will be made the same way. If the campaign gets very big, we have extensive shipping experience and fulfilling thousands of packages around the world is easy and trouble-free for us (we did this just a few months ago for our prior campaign). Furthermore, every package ships with tracking.

We have a proven track record of keeping backers updated, staying in communication with them and fulfilling quality products to our backers. We have solidly prepared for this campaign and have the experience necessary to successfully produce and fulfill PentaOrbiforms for all of our backers.

Support

1. Select this reward

Pledge US\$ 1 or more About US\$ 1.00

Good Karma!

THANK YOU for your support! Every pledge helps.

Less
Estimated delivery
18 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

2. Reward no longer available

Pledge \$26 or more About \$26

1 PentaOrbiform - Early Bird Special!

Stainless Steel

Choice of Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 102 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

3. Reward no longer available

Pledge \$28 or more About \$28

1 PentaOrbiform - Early Bird Limited

Stainless Steel
Choice of Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 149 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

4. Reward no longer available

Pledge \$29 or more About \$29

1 PentaOrbiform - Early Bird

Choose Copper or Brass
Choice of Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 37 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

5. Reward no longer available

Pledge \$31 or more About \$31

1 PentaOrbiform - Early Bird Limited

Choose Copper or Brass
Choice of Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 149 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

6. Select this reward

Pledge \$34 or more About \$34

1 PentaOrbiform

Choose Copper, Brass or Stainless Steel
Choice of Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
83 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

7. Reward no longer available

Pledge \$56 or more About \$56

2 PentaOrbiforms - Early Bird

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 21 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

8. Select this reward

Pledge \$59 or more About \$59

2 PentaOrbiforms - Early Bird Limited

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Limited 84 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

9. Select this reward

Pledge \$66 or more About \$66

2 PentaOrbiforms

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
5 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

10. Reward no longer available

Pledge \$84 or more About \$84

3 PentaOrbiforms - Early Bird

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 71 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

11. Reward no longer available

Pledge \$88 or more About \$88

3 PentaOrbiforms - Early Bird Limited

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 149 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

12. Select this reward

Pledge \$94 or more About \$94

3 PentaOrbiforms

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
38 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

13. Reward no longer available

Pledge \$115 or more About \$115

4 PentaOrbiforms - Early Bird

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Reward no longer available 1 backer
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

14. Select this reward

Pledge \$119 or more About \$119

4 PentaOrbiforms - Early Bird Limited

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Limited 15 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

15. Select this reward

Pledge \$124 or more About \$124

4 PentaOrbiforms

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
2 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

16. Select this reward

Pledge \$174 or more About \$174

6 PentaOrbiforms - Early Bird

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Limited 26 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

17. Select this reward

Pledge \$188 or more About \$188

6 PentaOrbiforms

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
0 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

18. Select this reward

Pledge \$249 or more About \$249

9 PentaOrbiforms - Early Bird

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
Limited 15 backers
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.

19. Select this reward

Pledge \$269 or more About \$269

9 PentaOrbiforms

Mix and match. Any combination of metals and finishes. Choose your favorites!

Metals: Copper, Brass & Stainless Steel.

Finishes: Mirror Polish, Satin, Machine.

Less
Estimated delivery
Ships to Anywhere in the world
1 backer
\$
Kickstarter is not a store.

It's a way to bring creative projects to life.