Again I am off on a project of my own related to design work I am doing.
Please move if this is the wrong forum for this question - I suspect it is not really College Level geometry (well I certainly am not ;-) )
Basically I want to reproduce a figure that I have grabbed a 3D render of. I need to do it in a vector drawing programme and need to know how to derive the angles and lengths of the sides.
The form is that of the three intersecting golden rectangles rotated in such a way as to produce the appearance of three intersecting planes that fit within a 3 Dimensional Icosahedron.
I reproduce the figures I am working from here:
In tracing the rasterised vector artwork above I find that the sides of the parallelograms are about 6.5 and 10.5 cm. When I use trig to find the top right apex interior angle it is 59.4° - or I assume 60° due to the perspective method used...
Is it the case that the matter of creating a parallelogram out of a golden rectangle does not in fact interfere with the properties of the object?
I figure that all I need to work out is how to take a golden rectancle and shear it in such a way that it is still a fibonacci shape...
I am working off the basis of a golden rectangle in the simplest way I can:
10cm x 16.18cm
Is this possible or is the very nature of shearing the golden rectangle to create the illusion of 3 Dimensions going to destroy the phi relationships - and if so can I just pick a suitable interior angle and then rotate three copies of the created parallelogram in such a way as to get the effect...
I will be then using colour and transparency blending to create a geometric logo/design element in stereo...
Many thanks in advance to anybody who can provide any (ph)insight
these are the constructs I have managed this afternoon using only very elementary assumptions about the geometries involved...