22 May 2013

WXYZ - 4 Intersecting planes - Triangular Planes

Four intersecting rectangular planes(Number of colors = Number of planes).
Two planes green and orange can be clearly seen. Other two yellow and purple lie pointing to us. I did this before trying 4 intersecting rectangular plane. This is an easy one. Fun to do. Assembly is also simple. Here's the reference given in David Petty's web page.

Reference: http://www.davidpetty.me.uk/origamiemporium/images/lam_wxyz.gif
No of Units: 4 * 3 = 12. 4 planes and 3 units in each plane.
Difficulty: easy to make units and easy to assemble. Very sturdy module
Paper used: I used regular color printer sheets.
Paper size: 5 inch x 5 inch square
Time taken: do not remember: but can be finished within 2 hour or even 1 hour.

If we consider one triangular plane, there are 3 units that makes a triangular plane. To calculate the angle between each unit, 360/3 = 120 degrees (similar to rectangular plane).
It can be proved that each triangular plane is an equilateral triangle (all angles of triangle = 60 degrees).

(Proof: We know that one angle is 120 degrees, the other two are 90 degrees. When we divide the basic unit into two parts, we get two triangles, one angle is 120/2 = 60 degrees, other is 90 degrees, so the third should be 30 degrees. Hence 30 x 2 = 60 degrees)

Assembly Technique: Join four color units by inserting one unit's flap in the others pocket. Continue joining remembering that all colors should be in a plane.

Next one I did was 5 intersecting planes.

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