Goldberg Polyhedron Mold Engine

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Project · Hearth Dome / Mold Cast
Geometry · GP(4,0)
☕ Buy me a coffee ↗Rev · 2026.05.25 · b10.b8f1450
A.01Dome Parameters
Preset
Truncated icosahedron at frequency 4, dualed to a Goldberg solid. The hemisphere resolves to just four repeating brick shapes — tractable for mold-making.
Symmetry
Pattern
Frequency4
162 total faces on full sphere
Interior Ø40″
Brick Thickness4″
Cut Angle90° (20″ tall)
Hemisphere — max floor area
Mortar Gap0.0″
No mortar — bricks butt directly.
A.02Door Opening
Cut arch openingArch Height2° (9″ from base)
Arch top above the dome floor. ~15° gives a classic mouth.
Arch Width20° (16″ across)
Half-angle of the arch — bigger = wider mouth.
▸ Auto-aligned to dome symmetry · cuts mirror L/R
A.03Arch Extension + Chimney
Show entry arch + chimneyArch Depth10″
How far the entry tunnel projects forward.
Arch opening auto-matches door cut; wall thickness follows brick thickness.
Chimney Ø6″
Chimney Height12″
Chimney In/Out0 mm
0 = centered on arch extension. + moves outward, - moves toward dome center.
A.04Display
Show brick edges
A.05Export STL
Full build setZip contains 11 unique bricks (one file per type). Cast each the schedule count of times.
Emboss labels & ↑ arrowBrick type + orientation arrow raised on the outer cap (visible when laid up). Recommended for scaled-down test prints.
All STL files exported in millimeters, oriented for direct 3D printing.
Safety · Builders proceed at their own risk. All safety concerns are solely the builder’s responsibility.
License · Mold STLs are the property of geohack.xyz and may not be used for retail sales or other commercial purposes.
Viewport · IsometricScale 1:1 · 40″ ID
Click face → highlight typeDrag → orbit · Scroll → zoom
B.01Dome Specifications
Total bricks90
Full bricks66
Cut bricks17
Arch bricks7
Unique shapes11
Outer Ø48″
Inner Ø40″
Footprint Ø49″ (+1.7%)
Wall thickness4″
Dome height20″
Floor area8.8 ft²
Cook volume9.8 ft³
PatternGP(4,0)
Sphere faces162
Pentagons12
Hexagons150
B.02Brick Schedule
▸ Full Bricks
Pentagon5-sided
Count× 5
Max span7.4″
Edges4.4″ / 4.4″ / 4.4″ / 4.4″ / 4.4″
Hexagon A6-sided
Count× 28
Max span8.4″
Edges3.5″ / 4.3″ / 4.5″ / 4.3″ / 3.5″ / 4.4″
Hexagon B6-sided
Count× 10
Max span8.8″
Edges4.3″ / 4.3″ / 4.5″ / 4.3″ / 4.3″ / 4.5″
Hexagon C6-sided
Count× 23
Max span8.8″
Edges4.3″ / 4.3″ / 4.5″ / 4.5″ / 4.3″ / 4.3″
▸ Cut Bricks · Rim
Cut A5-sided
Count× 5
SourceHexagon, clipped
Max span8.5″
Edges4.5″ / 4.5″ / 2.3″ / 7.6″ / 2.3″
Cut B5-sided
Count× 8
SourceHexagon, clipped
Max span8.4″
Edges4.3″ / 4.5″ / 2.0″ / 7.6″ / 2.3″
Cut C5-sided
Count× 4
SourceHexagon, clipped
Max span8.2″
Edges2.0″ / 4.3″ / 4.3″ / 2.0″ / 7.6″
▸ Arch Bricks · Opening
Arch A4-sided
Count× 2
Max span5.9″
Edges3.5″ / 2.2″ / 5.2″ / 1.0″
Arch B4-sided
Count× 2
SourceHexagon, clipped
Max span4.9″
Edges2.8″ / 2.3″ / 3.0″ / 3.7″
Arch C6-sided
Count× 1
Max span7.5″
Edges4.4″ / 1.0″ / 5.4″ / 1.0″ / 4.4″ / 4.4″
Arch D7-sided
Count× 2
Max span9.5″
Edges4.3″ / 4.3″ / 4.5″ / 4.5″ / 2.8″ / 3.1″ / 2.2″
Notes ·General SpecificationsSheet N.01
№ 01Geometry
A GP(4,0) Goldberg polyhedron is the dual of a Class I geodesic sphere built on the icosahedron at frequency 4. It carries exactly 12 pentagon faces and 150 hexagonal faces. Bricks crossing the cut plane are clipped into partial shapes — listed as “Cut bricks” with their own dedicated molds.
№ 02Brick Construction
Each brick is a curved panel 4″ thick, with the outer surface following the dome's spherical curvature. Material selection and any interior insulation layer are at the builder’s discretion.
№ 03STL Molds (mm)
Molds are thin-walled shells matching each brick's perimeter — open at both ends, tapered to flare outward going up. The cavity floor is flattened and an optional flange wraps the base, so the whole bottom rim sits flush on the print bed. Print without supports, cast on melamine. STLs are in millimeters.
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