Pentakis Dodecahedron Sphere

thingiverse

I've been looking for quite a long time for a method to produce a big, hollow sphere with a small printing volume. There are several different methods to achieve this (geodesic domes, Fibonacci sphere), but most of them will produce too many pieces of different shape and size. The pentakis dodecahedron is a catalan solid with 60 equal faces, a mix between a icosahedron and a dodecahedron. Five or six faces come together at the vertices and are linked with rings. It needs a total of 180 screws and nuts. For smaller spheres they are not really necessary, as the rings fit quite well. Pictured are two sizes with 30cm / 10cm outer radius and 27cm / 8cm inner radius,weighing 6kg / 750g without screws. The big sphere uses conical screws, the small one uses cylindrical screws. See: https://en.wikipedia.org/wiki/Pentakis_dodecahedron ********* **Pieces:** 60 x faces, printed 12 x 5er rings, printed 20 x 6er rings, printed 180 x M5 10mm countersunk screws, bought 180 x M5 nuts. bought ********** **Printing:** - Three different sizes are provided as stl. See below on how to create other sizes. - The pentakis dodecahedron sphere needs no support on no piece. - Filling 5%. No other special printing options were applied. ************************** **Building instructions:** - Start by pressing the nuts into to the designated holes of a face. If you have problems getting them in, pull them in with a screw. - Fix a face and a 5er ring together. Use the vertex between the two equal sides - Add the other four faces counterclockwise - Once you have three pentagons together you can start to join them with 6er rings. - You may have difficulties inserting the last rings of the last face. Eventually use a longer screw to pull them in. ****** **Parameterization:** - The difference between outer and inner radius defines the thickness of the faces. The inner radius must be small enough, to give your nuts enough space or = 300; //Outer Radius of ball ir = 270; //Inner radius of ball / inscribed sphere - If the difference between outer and inner radius is too big, your discs will be too small. Adapt them by changing the following values. dh = 5; //Disc (ring) height dro = 20; //Disc outer radius dri = 7.5; //Disc inner radius - Depending on the above settings you will need to adapt the screw size. You may or may not have enough space for a cylindrical screwhead (depending on disc height). The right size is choosen visually in preview. You mus see the screwhead in preview. sd = 4;//Screw diameter shd = 8;//Screw head diameter sl = 10;//Screw length shtype = CONIC; //Screw head type. Choose CONIC or CYLINDRIC - By definition a catalan solid has equal dihedral angles. change the sc setting according to your wishes. //Use this if you wish equal dihedral angles between faces and an inscribed sphere. //This will result in a smaller inner sphere sc = (3*phi+12)/19; //Use this if you wisch to habe all vertices on the circumsphere. //This will allow for a bigger inner sphere sc = sqrt(3)/sqrt(phi*phi+1);