curler units

8/14/2019 Curler Units

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Curler Units

Use small squares (max 7x7 cm) of stiff paper. Ordinary origami paper is too thin, but photocopy paper works ery well. !ake a waterbombbase and curl each of the flaps into a cone. "s shown in the top iew, all flaps are curled clockwise (left#handed folders may find it easier towork from a mirror image of these diagrams # sorry$)

%he paper should stay curled up as indicated (that&s why youneed heaier paper) so initially you&ll need roll up the flaps a bittighter than shown in the drawings as the curls will open outslightly when you let go.

%o assemble the units, gently ease one curl inside another curl.'ou can combine , , *, +... curls this way to create many#armed ortexes. 'ou can think of a #ortex as a triangle, a *#ortex is a square and so on. ombining the curls of a numberof these units into ortexes you can make seeral differentpolyhedra.

%he final drawing (below) shows a cuboctahedron. -or this,you&ll need units. /oin units in a #ortex. /oin the curlsalong the edges of this 0triangle0 and add more units to makeeach of these linked curls into a *#ortex.

ontinue building the cuboctahedron until you run out of units. %ake care neer to put more than onecurl of a unit in the same ortex. 1f you lose trackof the curls, 2ust remember that each square issurrounded by * triangles and each triangle issurrounded by squares.

1f this explanation doesn&t work for you, try thediagrams at the right. -irst you 2oin units in asub#assembly (which we simplify to a 0curly triangle0) and then 2oin * of these sub#assemblies as indicated in the big drawing on the right. %he arrows and numbers indicatehow many curls are 2oined at each position.

-urther experiments 3 %o make an icosidodecahedron (which consists of #ortexes and +#ortexes) you&ll need 4 units.onstruction is similar to the cuboctahedron but here each pentagon is surrounded by + triangles and each triangle issurrounded by pentagons. 5hen you make constructions with this many units, it&s a good idea to make the curls a littletighter (and looser if you use less units, though such sparse assemblies are not as attractie and stable. %he 6#unitoctahedron, for instance, is rather fragile because the curls are oerstretched).

'ou can construct other polyhedra this way (obious candidates are the (small) rhombicuboctahedron and the (small)rhombicosidodecahedron) but only if there are exactly * faces meeting at eery corner (ertex) of the polyhedron. %his isbecause the waterbomb base has exactly * flaps $

1f you really want to make polyhedra with faces meeting at the corners you could put curls of a unit in the same ortex or tuck awaythe fourth flap inside the waterbomb base or 2ust leae curl unconnected (if there is enough room in the ortex) but none of thesesolutions are ery elegant.

%o make the icosahedron (which has + faces meeting at each corner) we 2ust leae a hole where the+th face should go. "s it&s quite tricky to assemble, here&s another diagram to help you. 'ou use thesame * sub#assemblies as for the cuboctahedron, but put them -igure together in a slightly differentway. %he resulting figure is strangely irregular 3 it looks a bit like an icosahedron but not quite. %he0holes0 are pulled further apart than the 0filled0 triangular faces so the modular only has tetrahedralsymmetry (and is in fact closely related to the snub tetrahedron).

ere you see a strange property of these assemblies 3 the curls act as tiny rubber bands pulling theunits together, so that the structure settles at an equilibrium position where the tension in all the curlsis minimal (which is usually, but not always, quite a regular configuration).

-or the adenturous 3 " *#unit tetrahedron is 2ust possible. curls of each unit are 2oined in #ortexes along the tetrahedron&s edges, the fourth is unconnected. Or try the 8#unit deltoidal

icositetrahedron. "ll curls are 2oined in #ortexes and those corners of the icositetrahedron where faces meet are left as holes. %hat&s why we only need 8 units instead of 6. !ake a *#unit snub cube, either leaing the 6 square facesas holes or leaing 8 triangular faces as holes (choose those triangles not sharing any edges with the squares)



1 haen&t experimented with colours 3 1 prefer working in white as the shadows on thecured surfaces show up better. 1f you want to hae a go you could try folding yourwaterbomb bases from pre#coloured squares with a light#dark pattern as shown in thefigures on the right. %he cuboctahedron will then hae triangular ortexes in one colourand square ortexes in the other (this works for the icosidodecahedron as well). 1f youdon&t like using pre#printed patterns, get duo paper, blint9 it and then fold the blint9edtriangles to create the colour pattern you want to experiment with.

Herman Van Goubergen

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Kręciołkowe platónico.

Platónica módulo estándar Herman van Goubergena.

Octaedro (6 módulos).

Sześcioośmiościan (12 módulos).

Rhombicubooctahedron Cuboctaedro

(24 módulos).



Icosaedro de doce (! módulos).

"oce icosaedro rómbica #e$ue%o (6! módulos).

Poliedros con módulos personalizados Krystyna

urczyk.

"odecaedro (2! módulos).



Icosaedro (12 módulos).

Icosaedro truncado (6! módulos).

Octaedro truncado (24 módulos).



Cuboctaedro &ran dodecaedro (4'

módulos).

curler units

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