PARAMETRIC · 3D · STEP / STL / 3MF
Regular PolyhedronREGULAR POLYHEDRON
Generate any of the 5 Platonic solids by edge or circumscribed diameter, resting on a face. STEP, STL, 3MF.
- Shapes5 Platonic solids
- OrientationFace on the bed
- OutputSTEP · STL · 3MF · DXF
LIVE · REGULAR POLYHEDRON
ICOS · a20
SCALE 1:1 · mm
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CALCULATED · SPEC
AUTO-COMPUTED
F
20
Faces
a
20.00mm
Edge length
D
38.04mm
Circumscribed Ø
d
30.23mm
Inscribed Ø
V
17453.6mm³
Volume
A
3464.1mm²
Surface area
H
30.23mm
Print height
HOW-TO
How to generate a regular polyhedron STEP / STL file
- 1Choose the polyhedron.
- 2Choose edge length or circumscribed diameter and enter the size.
- 3The solid already rests on a face at z = 0, ready to print.
- 4Check the spec cards and any warnings.
- 5Download STEP, STL or 3MF — or send it to Orinovate for a quote.
What are the regular polyhedra?
A regular (Platonic) polyhedron has identical regular polygon faces with the same number meeting at each vertex. There are exactly five: tetrahedron, cube, octahedron, dodecahedron (pentagons) and icosahedron. This tool builds the exact planar solid from a vertex table — not a mesh approximation.
Formulas (edge a)
Surface: tetrahedron √3a², cube 6a², octahedron 2√3a², dodecahedron 3√(25 + 10√5)a², icosahedron 5√3a². Circumradius: a√6/4, a√3/2, a/√2, a√3(1 + √5)/4, a√(10 + 2√5)/4.
Specs at default parameters
| Parameter | Value | Range |
|---|---|---|
| Shape | Icosahedron (20) | Tetrahedron (4) / Cube (6) / Octahedron (8) / Dodecahedron (12) / Icosahedron (20) |
| Size by | Edge length (a) | Edge length (a) / Circumscribed Ø (D) |
| Size | 20 mm | 1–1000 |
| Faces (F) | 20 | — |
| Edge length (a) | 20.00 mm | — |
| Circumscribed Ø (D) | 38.04 mm | — |
| Inscribed Ø (d) | 30.23 mm | — |
| Volume (V) | 17453.6 mm³ | — |
| Surface area (A) | 3464.1 mm² | — |
| Print height (H) | 30.23 mm | — |
FAQ
Can I make tabletop dice?
Yes — the five solids are D4, D6, D8, D12 and D20. Typical D20 / D12 dice are 20–24 mm across the points, so use “Circumscribed Ø”. Add numbers in CAD with an emboss / engrave.
Why is it lying on a face?
A vertex-down polyhedron can't be printed stably, so the tool rotates it to rest on a face at z = 0 with one edge along X. Except for the tetrahedron, the top face is parallel to the bed too.
What are the volume formulas?
With edge a: tetrahedron a³/(6√2), cube a³, octahedron (√2/3)a³, dodecahedron (15 + 7√5)a³/4, icosahedron 5(3 + √5)a³/12.
Which software opens the regular polyhedron 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.