Archimedean Polyhedra

7/27/2019 Archimedean Polyhedra

1/13

Archimedean polyhedraHere are templates for making paper models for each of the 5 Platonicsolids and the 13 Archimedean semi-regular polyhedra . You are free to usethem for any non-commercial purpose, as long as the copyright notice oneach page is retained.

Here's a complete set of the Archimedean polyhedra:

I think that they are pretty straightforward to assemble without anyinstructions just cut them out carefully, fold along the black lines, and tape.In some cases you'll need to print multiple copies of a template. Theparenthesized numbers before each name tells you what each vertex shouldlook like: in a (3,4,3,4) cuboctahedron , for instance, each vertex should besurrounded by a triangle, a square, another triangle, and other square, in orderas you go around the vertex. Knowing this can be helpful when you're trying tofold the pieces up and figure out what pairs of edges match up.

For best results, print these templates out on cardstock, or print them onregular paper and use a pin to transfer the template to something heavier.Each template is fitted within the printable area of a Tektronix Phaser 360 colorprinter (which is what I used in making mine). If your printer has a smallerprintable area, some edges may get cut off. Sorry.
http://www.georgehart.com/virtual-polyhedra/platonic-info.htmlhttp://www.georgehart.com/virtual-polyhedra/platonic-info.htmlhttp://www.georgehart.com/virtual-polyhedra/platonic-info.htmlhttp://www.georgehart.com/virtual-polyhedra/archimedean-info.htmlhttp://www.georgehart.com/virtual-polyhedra/archimedean-info.htmlhttp://www.georgehart.com/virtual-polyhedra/platonic-info.htmlhttp://www.georgehart.com/virtual-polyhedra/platonic-info.html


2/13

All of the models have a common edge length, so relative sizes are meaningful.The squares on the smallest (the cuboctahedron) are the same size as thesquares of the largest (the truncated icosidodecahedron). This means thatsome of the polyhedra turn out very large, and take several sheets of paper.The largest one requires seven pages of template and is roughly nine inches indiameter when completed.

Start by making the Platonic solids and the smaller Archimedeans first. Thelarger ones are trickier to cut out and assemble.

If you don't have it already, you'll need the free Adobe Acrobat Reader .

Platonic solids(3,3,3) tetrahedron

(4,4,4) cube

(3,3,3,3) octahedron

(3,3,3,3,3) icosahedron

These four all fit on the same page; by printing out one copy of the page youcan make them all.

platonic1.pdf
http://www.adobe.com/products/acrobat/readstep.htmlhttp://www.adobe.com/products/acrobat/readstep.htmlhttp://www.adobe.com/products/acrobat/readstep.htmlhttp://isotropic.org/polyhedra/platonic1.pdfhttp://isotropic.org/polyhedra/platonic1.pdfhttp://www.adobe.com/products/acrobat/readstep.htmlhttp://isotropic.org/polyhedra/platonic1.pdfhttp://www.adobe.com/products/acrobat/readstep.htmlhttp://isotropic.org/polyhedra/platonic1.pdfhttp://www.adobe.com/products/acrobat/readstep.html


3/13

(5,5,5) dodecahedron

platonic2.pdf

Archimedean semi-regular polyhedra

(3,6,6) truncated tetrahedron

(3,4,3,4) cuboctahedron

These two fit on the same page; by printing out one copy of the page you can

make them both. The cuboctahedron is the one on top.
http://isotropic.org/polyhedra/platonic2.pdfhttp://isotropic.org/polyhedra/platonic2.pdfhttp://isotropic.org/polyhedra/platonic2.pdfhttp://isotropic.org/polyhedra/platonic2.pdfhttp://isotropic.org/polyhedra/platonic2.pdf


4/13


5/13

(3,8,8) truncated cube

This comes in two identical pieces; you need them both to make a singlepolyhedron.

388.pdf

(3,4,4,4) rhombicuboctahedron

A single copy of this page will fold up into the rhombicuboctahedron.

3444.pdf
http://isotropic.org/polyhedra/388.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/388.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/388.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/388.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/388.pdfhttp://isotropic.org/polyhedra/3444.pdfhttp://isotropic.org/polyhedra/388.pdf


6/13

(4,6,8) truncated cuboctahedron

Print two copies of this page to get four pieces, two of which are individualsquares. The bottom side of the bottom hexagon of one big piece fits upagainst the free side of the top square of the other piece, leaving a square holeon each side.

468.pdf
http://isotropic.org/polyhedra/468.pdfhttp://isotropic.org/polyhedra/468.pdfhttp://isotropic.org/polyhedra/468.pdfhttp://isotropic.org/polyhedra/468.pdfhttp://isotropic.org/polyhedra/468.pdf


7/13

(3,3,3,3,4) snub cuboctahedron

This shape comes from just a single piece. You can imagine creating this shapeby taking the (3,4,4,4) rhombicuboctahedron and turning each yellow squareinto two yellow triangles. That's why there are two different colors of triangle inthis model the blue ones are the eight blue triangles already present in therhombicuboctahedron.

33334.pdf
http://isotropic.org/polyhedra/33334.pdfhttp://isotropic.org/polyhedra/33334.pdfhttp://isotropic.org/polyhedra/33334.pdfhttp://isotropic.org/polyhedra/33334.pdf


8/13

(3,5,3,5) icosidodecahedron

This comes in two identical pieces; you need them both to make a singlepolyhedron. This is relatively easy to cut out and assemble, but the foldingstage can be tricky.

3535.pdf
http://isotropic.org/polyhedra/3535.pdfhttp://isotropic.org/polyhedra/3535.pdfhttp://isotropic.org/polyhedra/3535.pdfhttp://isotropic.org/polyhedra/3535.pdfhttp://isotropic.org/polyhedra/3535.pdf


9/13

(5,6,6) truncated icosahedron

Everyone's favorite polyhedron the shape of soccerballs and buckyballs.

You need two copies of this page. Notice how each big piece consists of acentral pentagon with double-hexagon "arms" radiating out, except that one of the arms has only a single hex. This is where the individual hexagon should beattached. Once this is done you'll have two star-shaped pieces that fold up intobig bowls, and then the rims of the bowls can be matched up.

The most difficult part of making this one is cutting it out, because of thoselightning-bolt-shaped "alleyways" that come in from the perimeter.

566.pdf


10/13

(3,10,10) truncated dodecahedron

The soccerball's evil twin. You'll need four copies of this page to put it together(decagons take a lot of room on the page!).

If you're having trouble figuring out how the pieces fit together, read the notesfor the last shape, the (3,3,3,3,5) snub icosidodecahedron.

31010.pdf


11/13

(3,4,5,4) rhombicosidodecahedron

Print out two copies to get the six total pieces you'll need. The two star shapesfold up into shallow bowls. Two copies of the snake plus the two individualsquares can be strung together to make a belt around the equator that joinsthe bowls together just continue the alternating triangles and squarespattern.

3454.pdf


12/13


13/13

(3,3,3,3,5) snub icosidodecahedron

Print two copies to make four identical pieces. This is probably the most difficultto assemble because the faces are small and the dihedral angles are large.

Each of the four pieces has threefold rotational symmetry (once it's taped upinto a shallow bowl), except for a single blue triangle that sticks out in oneplace. This is also the case for the (3,10,10) truncated dodecahedron; the fourpieces fit together in analogous ways. You should be able to fit two piecestogether to make a kind of U-shape; a second identical U-shape will completethe polyhedron with a 90-degree rotation (think of how a baseball is stitchedtogether from two pieces). Keep in mind that a blue triangle should be adjacentto three yellow triangles, and that each yellow triangle should be adjacent toexactly one blue triangle, one yellow triangle, and one purple pentagon.

33335.pdf

last edited Saturday, 11 November 2006

Archimedean Polyhedra

Documents

Transcript of Archimedean Polyhedra