Net for Truncated Octahedron.

Net for Truncated Octahedron

14 faces (06 squares, 08 hexagons), 24 vertices, 36 edges. Octahedral (02, 03, 04-fold) symmetry.

Construction drawing

Method:

1. On a long horizontal draw a circle centre O (the diameter of your circle should be just less than one sixth of the width of your sheet). Construct the vertical axis through O to give you points A and B. The rest of the construction is drawn using only the original radius.

2. Draw arcs from A to find C and D; and from B to find E and F. This gives you the first hexagon ADFBEC.

3. A line through DC extended to the left, and an arc from C will find G. Similarly, a line through FE and an arc from E will find H. GCEH is the first square. Find squares AJKD and FMLB in the same way by extending EA, BD; and AF, CB.

 Illustration of the net drawn out on card and cut out.

4. Pairs of arcs from A and C, B and E, D and F will cross to find new centres O², O³ and O4. On each of these new centres draw a circle, and walk the radius round each circle to find the points of the hexagons.

5. Square NQRP is found by extending lines through CD and EF to the right, and drawing arcs from N and P to find Q and R. Centre O5 is found by drawing arcs from Q and R to cross. With this new centre established, the rest of the figure is constructed in the same way as the first half.

6. Add tabs and mark the cut and fold lines as shown.

7. Cut out along the solid lines: score along the dashed lines. Fold upwards along the scored lines.

8. Glue carefully and progressively (tabs inside) - one or two tabs at a time. Clean up and decorate as you wish.👍

Note:-

The net can be drawn in two halves, both identical apart from the tabs. You will also need one additional tab to join the two halves together. The dotted line on Figure between points N and P shows this.

 Illustrations of the model partially assembled (above left and middle); complete (above); and a coloured version (below).