Nets for Building Models

Here are some collections of nets for various polyhedral projects. For the geodesic models, good references are Spherical Models by Magnus Wenninger and Polyhedra and Geodesic Structures by Vincent J. Matsko. (See the "References" page.)

Alphabetical List of Nets

Compound of Five Octahedra
Compound of Five Tetrahedra
Dodecadodecahedron
Geodesic Dodecahedron
Geodesic Dodecahedron (with Pentagrams)
Geodesic Icosahedron (4-frequency)
Geodesic Icosahedron (8-frequency)
Geodesic Icosahedron (Class II, 4-frequency)
Geodesic Icosidodecahedron
Geodesic Octahedron
Geodesic Rhombitruncated Icosahedron
Geodesic Snub Dodecahedron
Geodesic Tetrahedron
Geodesic Truncated Dodecahedron
Geodesic Truncated Icosahedron
Platonic Solids
Polygons (for Archimedean Solids)

Compound of Five Octahedra

This is a stellation of the icosahedron. It is not as tricky as the compound of five tetrahedra, but does require patience. See 23 in Polyhedron Models.

Download the net for the compound of five octahedra.

Compound of Five Tetrahedra

This is a stellation of the icosahedron. See 24 in Polyhedron Models. It is a tricky model to make, so don't be discouraged if your last piece doesn't fit together perfectly. Not for beginning model builders!

Download the net for the compound of five tetrahedra.

Dodecadodecahedron

This uniform polyhedron is model 73 in Wenninger's Polyhedron Models. As with many nonconvex models, this model takes patience. You will have to add your own tabs on these nets.

Download the nets for the dodecadodecahedron.

Geodesic Dodecahedron

A geodesic dodecahedron may be formed by projecting a dodecahedron onto a sphere, and then subdividing each pentagon into five congruent spherical triangles. This model may be easily assembled by first making groups of five spherical triangles, and then assembling them as you would a dodecahedron. To make the spherical pentagons, just glue five spherical triangles together so that their tabs all meet at the center of the pentagon.

Download the net for the geodesic dodecahedron.

Geodesic Dodecahedron (with Pentagrams)

Begin with a regular dodecahedron. Inscribe pentagrams (stars) in the pentagonal faces, and then project both the pentagons and pentagrams onto the circumsphere to form this geodesic model. It is similar to Photo 21 (p. 61) of Wenninger's Spherical Models, although a simplified version (compare 120 spherical triangles and 12 spherical pentagons to the 360 spherical triangles needed to build the model in Photo 21).

If you study Photo 21, this model should not be difficult to build. Note that the largest arcs are the projected edges of the dodecahedron; this should be a useful guide. The small pentagons are in the centers of the larger dodecahedral pentagons, and the other triangles fill in the remaining spaces.

Download the nets for the geodesic dodecahedron (with pentagrams).

Geodesic Icosahedron (4-frequency)

Not so challenging as its 8-frequency companion, this model requires just 320 individual spherical triangles of 5 distinct types. Bands are labelled numerically as in Figure 48 (p. 95) of Wenninger's Spherical Models. Although not individually labelled, the bands adhere to the following scheme: in Table 4, the arc in the third column of the list of bands is always next to the tab. You can easily check this by noting that in a circle, larger angles subtend larger chords, so you can measure chords to find out which angle is which.

The finished model will be approximately 14 inches (36 cm) in diameter.

Download the nets for the 4-frequency geodesic icosahedron.

Geodesic Icosahedron (8-frequency)

This is a very challenging model to make, requiring 1280 spherical triangles of 15 distinct types. Bands are labelled numerically as in Figure 50 (p. 97) of Wenninger's Spherical Models. Although not individually labelled, the bands adhere to the following scheme: in Table 6, the arc in the third column of the list of bands is always next to the tab. You can easily check this by noting that in a circle, larger angles subtend larger chords, so you can measure chords to find out which angle is which.

The finished model will be approximately 14 inches (36 cm) in diameter.

Download the nets for the 8-frequency geodesic icosahedron.

Geodesic Icosahedron (Class II, 4-frequency)

This 4-frequency model is a Class II icosahedron, meaning that the goedesic arcs are perpendicular to (rather than parallel to) the edges of the parent icosahedron. See Figure 55 (p. 110) of Wenninger's Spherical Models for a more detailed study.

The finished model will be approximately 10 inches (25 cm) in diameter.

Download the nets for the 4-frequency Class II geodesic icosahedron.

Geodesic Icosidodecahedron

For this model of the geodesic icosidodecahedron, the triangles are simply projected onto the circumsphere. The pentagons are divided into five congruent isosceles triangles. For more information, see pp. 80-81 of Wenninger's Spherical Models.

Download the net for the triangular faces.

Download the net for the pentagonal subtriangles.

Geodesic Octahedron

This model is made of 48 congruent spherical triangles modelled on the symmetry of the octahedron. For a complete description, see pp. 3-11 of Wenninger's Spherical Models.

Download the net for the geodesic octahedron.

Geodesic Rhombitruncated Icosidodecahedron

See Chad holding a model of his rhombitruncated icosidodecahedron.

Download the net for the square subtriangles.

Download the net for the hexagonal subtriangles.

Download the net for the decagonal subtriangles.

Geodesic Snub Dodecahedron

These nets allow construction of the model in Photo 36 (p. 83) of Wenninger's Spherical Models. For this geodesic version of the snub dodecahedron, the triangles are kept intact, while the pentagons are subdivided into five isosceles spherical triangles.

Download the net for the triangles.

Download the net for the pentagonal subtriangles.

Geodesic Tetrahedron

This geodesic tetrahedron is Photo 1 (p. 3; see also pp. 9-12) of Wenninger's Spherical Models. Only 24 spherical triangles are necessary, so it is one of the simplest of all geodesics to build.

Download the net for the geodesic tetrahedron.

Geodesic Truncated Dodecahedron

See James holding a model of his truncated dodecahedron.

Since subdividing the spherical triangles of the truncated dodecahedron into six subtriangles would make them too small, James decided to subdivide them into only three smaller triangles.

Download the net for the decagonal subtriangles.

Download the net for the triangular subtriangles.

Geodesic Truncated Icosahedron

These nets allow you to create a geodesic truncated icosahedron, Photo 35 (p. 82) in Wenninger's Spherical Models. Spherical pentagons are subdivided into five isosceles spherical triangles, and spherical hexagons are subdivided into six isosceles spherical triangles.

Download the net for the pentagonal subtriangles.

Download the net for the hexagonal subtriangles.

Platonic Solids

Download the nets for the Platonic solids.

Polygons (for Archimedean Solids)

The faces of Archimedean solids are regular polygons. The polygons in the nets below all have an edge length of 1.5in (3.8cm). They may be used to build all the Archimedean solids.

Congruent faces are often adjacent, so some nets are given with polygons meeting edge-to-edge. You will have to draw in your own tabs (if necessary) before scoring and cutting.

Download the net for the triangles.

Download the net for the squares.

Download the net for the pentagons.

Download the net for the hexagons.

Download the net for the octagons.

Download the net for the decagons.