![]() Beware: you can't use the old A-B-C-D-E formula that we use for single pentagons. Try grouping the 12 pentagons into clusters, and let each repeating shape roam not-just-around-one-tile, but take up several adjacent tiles: 6 groups with 2 pentagons each, 4 groups of 3 pentagons each, 3 groups containing 4 pentagons each, and 2 groups with 6 pentagons in each group. Why're we using tracing paper? Because we have to be sure the borders along both pentagons' A-sides are identical, and both Bs, Cs, Ds, and Es.įor extra fun, instead of treating a single pentagon as the basic unit, try using a group of pentagons as the basic unit. Draw a squiggly borderline between the paired sides. Letter their sides, and then match them up, one pair of sides at a time. To make your own dodecahedron tessellation, cut out 2 pentagons on tracing paper. In the cat tessellation at the top of this page, the tall gray cat is on side "A" of each pentagon- see that every tall gray cat matches up with another tall gray cat on another pentagons. ![]() Similarly, Side B fits with another pentagon's Side C (and vice versa), and side D fits with E (and vice versa). See how Side A on one pentagon matches up with A on the pentagon next to it. Next, press your pentagons together, flat on a table, like the picture at left. Write "A, B, C, D, E", one letter per pentagon side, in (clockwise or counterclockwise) order. To figure that out, just lightly write a letter on each side of your pentagons like I've done in the picture at left. For a "dodecahedron", the only trick is to know which pentagon sides will touch one another when the "dodecahedron" is assembled. Finally, glue the two cup-shaped halves of the dodecahedron together.ģD tessellation really isn't difficult. At this point, you'll have two cup shapes of 6 pentagons each. (See the middle picture on this page.) Wait until they dry, then glue the petals together and let them dry. Put one in the center of each group and glue its edges to 5 pentagons around its edges, so it looks like a flat flower with five petals. Hint: separate the 12 pentagons into two groups. ![]() Print it 12 times, color the cats, and glue the 12 pentagons together as shown in the top picture on this page. Just print this PDF file of a single pentagon with cat outlines. You'll need scissors, glue, a printer, and paper. Is easy to make, and an ideal 3D geometry project. ![]() This paper or cardboard 12-sided 3D tessellation by Seth B.
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