PARAMETRIC · 3D · STEP / STL / 3MF
OloidOLOID
Generate an oloid — the convex hull of two perpendicular circles — from one diameter. STEP, STL or 3MF.
- Built fromHull of 2 circles
- Area= sphere of same r
- OutputSTEP · STL · 3MF · DXF
LIVE · OLOID
⌀40
SCALE 1:1 · mm
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CALCULATED · SPEC
AUTO-COMPUTED
V
24419.3mm³
Volume
A
5026.5mm²
Surface area
L
60.00mm
Overall length
s
125.66mm
Travel per roll cycle
HOW-TO
How to generate a oloid STEP / STL file
- 1Enter the generating-circle diameter.
- 2The model is centred on the origin and rests on z = 0.
- 3Check the spec cards and any warnings.
- 4Download STEP, STL or 3MF — or send it to Orinovate for a quote.
What is an oloid?
Discovered by Paul Schatz in 1929: place two circles of radius r in perpendicular planes so that each passes through the other's centre (centre distance r). Their convex hull is the oloid. Its surface consists of straight rulings and is developable.
Modelling and formulas
Rulings join the circles using the Dirnböck–Stachel correspondence cos t = cos s / (1 + cos s); four smooth patches are sewn into an exact solid. Length 3r, width and height 2r; surface A = 4πr²; volume V = 3.0524184684·r³.
Specs at default parameters
| Parameter | Value | Range |
|---|---|---|
| Circle diameter (D) | 40 mm | 2–1000 |
| Volume (V) | 24419.3 mm³ | — |
| Surface area (A) | 5026.5 mm² | — |
| Overall length (L) | 60.00 mm | — |
| Travel per roll cycle (s) | 125.66 mm | — |
FAQ
What is special about the oloid?
Its surface is developable — it unrolls flat onto paper without stretching. Rolling on a table it wobbles forward and every point of its surface touches the ground, which is why it is used for water-mixing devices, fidget toys and desk sculptures.
What are its volume and surface area?
With circle radius r: A = 4πr², exactly the area of a sphere of the same radius, and V ≈ 3.0524·r³. For D = 40 mm (r = 20): A ≈ 5,026.5 mm², V ≈ 24,419 mm³.
How should I print it?
It touches a plane along a single line, so use tree supports on FDM or flatten 0.5–1 mm off the bottom in CAD. You can also split it along a symmetry plane and print two halves.
Which software opens the oloid STEP file?
STEP (AP214) opens in Fusion 360, SolidWorks, FreeCAD, Onshape and Rhino. STL / 3MF import directly into Bambu Studio, PrusaSlicer or Cura.
Is it free?
Yes — no sign-up, no fees. Need a physical part? Send it to Orinovate for an instant quote in FDM, SLA, SLS, MJF or CNC.
Related generators
Need a physical part?
Send the model straight to Orinovate's instant quote: FDM, SLA, SLS, MJF, metal printing and CNC, made in Hsinchu, Taiwan.
About STEP / STL / 3MF / DXF
- STEP (.step / .stp, AP214) keeps exact dimensions and surfaces for editing in Fusion 360, SolidWorks or FreeCAD.
- STL and 3MF are triangle meshes that import directly into Bambu Studio, PrusaSlicer or Cura.
- DXF is the top-view 2D outline, ready for laser cutting, waterjet or CNC routing.
- All models are in millimetres at true scale.