Orbiforms are interesting for the way they stand at the intersection of science and fun, like a slinky, or a Newton’s cradle. They’re engaging, handsy, and boost attention while relieving stress. What are they specifically? They’re constant-width solids… or solids that aren’t completely spherical, but roll as smoothly as a sphere does (the GIF down the page shows you exactly what I mean). It was commonly accepted for the longest time that the sphere was the only solid of constant width, i.e., a solid that could rotate freely and smoothly without any bumps. However, constant width solids or Orbiforms were initially discovered by Da Vinci in the 16th century, and further explored by Leonard Euler in the 18th century (AltDynamic even created a series of these solids which they made available on Kickstarter).
The PentaOrbiform is the latest form to make that list of fixed-width solids. Designed by AltDynamic, the solid comes with the silhouette of a pentagon, and magically rolls with the smoothness of a sphere, but features a non-spherical design and even comes with edges. The main difference is the center of mass of the PentaOrbiform is not central like a sphere, so it doesn’t continue rolling unless a force remains on it.
While we don’t want to dwell too much on the mathematics of it (I promised that this would be fun too), the PentaOrbiform is a bafflingly enjoyable sculpture that sits on your desk, for you to roll around occasionally as you marvel the strange laws of geometry. Each PentaOrbiform is precisely machined from a block of metal and comes in three materials as well as three finishes. Choose between steel, brass, or copper and between a machined finish, or a mirror finish or even a matte/satin finish. You’ve even got the option of getting yourself a display stand for the PentaOrbiform, but in my opinion, it’s best kept directly on your desk, for you to roll around as you watch your stress melts away!
Designer: AltDynamic
The PentaOrbiform by AltDynamic is a math-based sculpture that rolls like a ball without the smooth edges.
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…). AltDynamic used this as inspiration for the name PentaOrbiform.
Math Talk
The PentaOrbiform is inspired by the form of the pentagon and 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. 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
PentaOrbiforms will be CNC machined from solid bars of stainless steel, copper and brass. AltDynamic will NOT be casting them! Casting would not provide them with the batch consistency, surface finish and quality they want to achieve and also would not be as dimensionally precise as machining. The pictures below show the nine different options.
Copper with Surface Finishes: Satin, Mirror Polish, Machine
Brass with Surface Finishes: Satin, Mirror Polish, Machine
Stainless Steel with Surface Finishes: Satin, Mirror Polish, Machine
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.
Machine Finish: 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.