My Brain has been mathematically idle for too long that it takes more time to process simple addition..!
Hence this easy mind refreshing exercise,
CONSTRUCT A TRUNCATED ICOSAHEDRON..
wikipedia links to familiarise with these shapes..
I dint take any reference coz it'll spoil the joy of making mistakes ;) I guess it's easier to construct with penatagons & hexagons, but more challenging and all the more fun to watch the actual transition happening. . So I went the "triangles & penatagons" way..
To begin with, I've cut 20 equilateral triangles of side 6cm (leaving 0.5cm space all around for the flaps)
I've made a template out of cardboard to save the trouble of measuring each time.!
Here comes the icosahedron, 20 triangular planar surfaces with 12 vertices.
I've used staples as am gonna redo it all :)
(Did you know: many viruses show icosahedral symmetry??! )
Now comes the fun part of the transition. I've folded the corners of triangles at 2cm (one-third of total edge length) so the triangles get converted to regular hexagons of size 2cm & when arranged in the same way like before, leaves a pentagon at each of the 12 vertices.
I've cut 12 pentagons of side 2cm out of black cardstock, (i used the angle method,72° to construct it)
stuck everything & ta da... I've got an almost sphere now :)
initially I tried to stick two flaps together which dint work out very well.. later on I cut one of the flaps accordingly as I added each hexagon &stuck it flat with the other side.. Things were much easier then..!
with acrylic colors & fine liner pens, corrected the imperfections, added outlines for more definition & completed with a coat of sealer :)
Done. It seems functional but can't be sure until it tears apart :D
Had so much fun doing this & dats more satisfying than anything else :)
Thanks for your time & patience :)