Net for the Octahedron (The Platonic Solids of Air)
08 triangular faces, 06 Vertices, 12 edges, Octahedral (2,3,4 fold) symmetry.
1. Draw a circle with centre O - (judge the position on the sheet as shown, to allow space for top point E).
2. Draw a long horizontal through the centre of the circle parallel to the bottom edge of the sheet.
3. Along the horizontal, with the same radius, draw 2 more circles with centres B and C, and 02 semicircular arcs (shown dashed) centres A and D.
4. Using circle intersection points, draw out the net as shown on facing page.
5. Add tabs as shown: the cut angle can be obtained with reference to points on the drawing as shown. Judge the width by eye.
6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully (tabs inside) starting with tabs marked 1. Clean up and decorate as you wish.
Net for the Icosahedron (The Platonic Solids of Water)
20 triangular faces, 12 Vertices, 30 edges, Icosahedral (2,3,5 fold) symmetry.
Illustrations of the net drawn out on card and cut out. (B)
Method:
1. Draw a circle centre O just in from the edge of the sheet and with a radius no more than one sixth of the width of your sheet (see Figure A).
2. Draw a long horizontal through the centre of the circle parallel to the bottom edge of the sheet.
3. Draw 04 more circles along the horizontal overlapping by half a diameter each time. Draw semicircular arcs at the extremes to left and right (shown dashed).
4. Using circle intersection points draw our the net as shown above.
5. Add tabs as shown using points on the drawing as guides to angle them off.
6. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines. Glue carefully and progressively together (tabs inside). I find it easier to glue one or two tabs at a time, and then pause. Clean up and decorate as you wish.👍
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