Different approach to design a lesser circle dome

[Levente Likhanecz]

With Sketchup i draw a 20 segment circle (20 is a must for this example).
I select "circle" to tool, then in the right corner of tray of the SU immediately displayed the sides number (24 default). Before you anchor the center of the circle you can type on the keyboard 2, 0, enter. what you type in this state, all go in that tray field.
If you made mistype, after the enter can type again, type, again...
The "circle tool" SU cursor will popup temporary, what number will be used.
Once you have drew the circle and the tray is expecting radius to correct by hand typing, you can type exact figures.

Next i want to rotate up a semi circle (yellow part) to the intersection point with the red colored semicircle, to form an equilateral triangle 2-2-2 segment sides:

With SU i can not make it directly (maybe it is just me) so first i have to create a "guide point" 

with the arc tool, from rotating center to the 2nd sgment tip radius, with the erected line that represent the intersection line of the small circle plane, and the vertical plane.
　

　

Then i rotate the yellow semicircle 5x 72 degrees apart on the equatorial plane.
and i get the full great circle frame of an icosahedral dome

in case you have a good length of pipe physically is less difficult to intersect them.

  　

once i have the great circle frame, it is interesting to place into it the icosahedron golden rectangles, and see where i have cardinal points, and cardinal lines:

i will attach the skp file of this last pic in the next message.
next message i will detail the lesser circle of this design, how to find it, and how to segment it.

[Levente Likhanecz]

here is the last wireframe skp file

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[Levente Likhanecz]

From the 2-2-2 segment equilateral triangles the 1-1-1 segments lay on the lesser circle plane (colored)

this plane's center is just above the equatorial plane (in my case on the blue axle) and the radius is on that plane till the vertices (lines on the colored poligon)

then i draw that poligon through the similar vertices pinky, then the 2 planes' intersecting line:

on that greenish-yellowis plane i make the intersect point by the lesser circle radius with  "arc tool".

i rotate the magenta arc clockwise to the next 2-2-2 triangle vertice (on the greenish plane's center)　

so the ends of the arcs mark the penta side (and the remaining strut as well)


On the lesser circles this pattern will repeatedly go around (the the great circle all the same circumference / 20 segment equal struts)

like this
　

　

time to populate it:
　

remains to connect the blue pentas (to get the icosa triangle).