5 Scalable Seamless Polyhedrons | Tutorial | 127 to 272 Neodymium Magnetic Balls

A quick video guide to building 5 different seamless and scalable 1 layer polyhedrons made from neodymium magnetic balls. Seamless means all the balls in each shape interlock closely with opposite polarity, instead of lining up in parallel and creating visible seams all over, ('seamed' subunits are better suited for interconnecting into larger structures). Scalable means they can each be built in multiple sizes. Although they are only hollow and 1 layer thick, these are nice and strong and stable once completed with an almost fabric-like quality.
It takes a bit of practice and skill to get familiar with these structures, make the pieces to the right size, and fit them together correctly, so don't give up if they seem tricky at first!

1) 0:18 Pentagonal Bipyramid - Edge 6 - 127 balls.
Build a pentagon 'hill' of outer edge 6 balls, and a pentagon 'valley' of edge 5 balls. This gives correct polarity from the same end of the line of magnets. Connect the smaller valley to the hill pentagon carefully as shown. To change scale, choose any outer edge length N pentagon hill of magnets and build the opposite side pentagon valley to edge N-1 magnets.

2) 1:31 Rhombic Icosahedron - Radius 4 - 182 balls.
This UFO-like shape has 20 rhombic (diamond shaped) faces. Start by building a pentagonal 'hill' of edge 7, and then a pentagonal 'valley' of edge 6, then connect the corner of the valley pentagon to the centre of the odd numbered hill pentagon edge. This produces rhombic edges of 4 balls in the completed shape, which I call radius 4. To build in a different size, you can only choose an odd number for the pentagonal hill edge N, and build a pentagonal valley of edge N-1, to produce rhombic faces of radius (N+1) ÷ 2.

3) 2:41 Rhombic Dodecahedron - Radius 5 - 194 balls.
This shape has 12 rhombic (diamond shaped) faces that are somewhat convex, so that it also resembles an octahedron of 8 triangular sides. The radius 5 refers to the number of balls forming each rhombic edge in the finished shape.
Build a 4 sided pyramid 'mountain' to outer edge 6, then build 4 edges of 5, 4, and 3 around the outside. Pinch each edge of 3 into vertices. Build a 4 sided upside down pyramid 'valley' to edge 7, and then connect the corner of this into the corner of the mountain and fold the pieces together. Add a magnet to the top and one to the bottom to complete the shape.
To scale this shape up or down, choose a rhombic edge radius of R, build a 4 sided pyramid to outer edge R + 1, add edges of R balls to all 4 sides and then keep adding -1 ball edges to all 4 sides down to edge 3, and pinch these 4 edges of 3 balls into vertices. Now build a 4 sided valley to edge 2R - 3, and connect the corners of this valley pyramid to the mountain one as shown. Requires a total magnet count of 12 × (R-1)^2 + 2.
Thanks to Boyd Edwards for his excellent tutorial and help with the math for this shape:
   • Hollow Octahedron Tutorial: Seamless Desig...  

4) 5:03 Icosahedron - Edge 6 - 252 balls.
Build a pentagonal 'hill' and 'valley' to outer edge 6 from the same line of magnets. Then add 4 rings of 25 balls to one pentagonal pyramid. Add the bottom pyramid so the corners form triangles of edge 6 as shown and complete the icosahedron.
To scale up or down, choose an edge N, build a hill and valley pentagonal pyramid of outer edge N, add N-2 rings of 5(N-1) balls, and connect the 2nd pyramid to form triangular faces of edge N. Edge 7 requires 362 balls, edge 8 requires 492 balls. You can also build it smaller (edge 5, 4 or 3).

5) 6:21 Rhombic Triacontahedron - Radius 4 - 272 balls.
This shape has 30 rhombic or diamond faces in a sphere-like formation. The radius 4 refers to the number of balls along each rhombic edge in the final shape.
Build a hill and valley pentagonal pyramid of outer edge 7 from the same line of magnets. Add a ball to the centre of each edge of the pentagonal hill pyramid and slightly pinch. Then complete 2 zigzag layers of 30 balls each. Carefully attach the 2nd pentagonal pyramid (the valley one) by corners into zigzag centres as shown.
To scale up or down, you can only choose an odd number for the pentagonal pyramid outer edge. Edge odd number N produces a rhombic triacontahedron of radius R = (N + 1) ÷ 2.
The odd number edge N required = radius 2R - 1.
The number of zigzag layers required between pyramids = (N - 3) ÷ 2, or R - 2.
The number of balls per zigzag layer is 5(N - 1).
Edge 9, radius 5 requires a total of 482 balls. edge 11, radius 6 requires 752 balls. A smaller one is edge 5, radius 3, which requires just 122 balls.

Music track is Passing Time by Kevin MacLeod, from the YouTube free audio library.

#ledwatchman #Neocube #Neoballs #Nanodots #ZenMagnets #Speks #Buckyballs #NingoBalls #CyberCube #KlikyBalls #howto