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The 20 minute 3D dodecahedron, lots of pics- dialup beware



I read the post a few week ago and found it a dandy little puzzle
First off I didnt even know what a dodecahedron was, and had to look it up
Second, no site could tell me the angle of intersection with the separate pentagons so I had to do all calculations by a relative point/object. That means you can put the calculator away and let CAD do all the number crunching

Make a flat 2D pentagon, trace the path of the adjactent pentagons, continue with simple wireframe, then create a large solid and slice it down using the wireframe as a reference.


My AutoCAD timer read 20 minutes when I was done so lets see how we fare

1st pic
Starting off with a 2D pentagon(red) and mirrored 2 more along the edges(white)
Perpendicular to the mirror lines we draw a new set(green) the the extension lines help to show which mirror line they each correspond to(yellow)
Also, all the tools you will use for this are shown (blue)

2nd pic
Now draw circles along the perpendicular lines from above (blue and green respectively)
These map the side points of the side pentagons if they each flowed around 360 degrees around the mirror line

3rd pic
We're not interested in the entire course of the points, but only where they intersect (magenta)

4th pic
Now array the lines around the center point

5th pic
Now we are mapping the final point on the adjacent pentagon (blue) by reference of the first pentagon (red)



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I forgot all new threads had to be approved...

6th pic
Simple array around the center point
The top half wireframe is done

7th pic
Now copy the whole thing
Next, rotate the newly copied objects 180 degrees (see pic for direction)

8th pic
Move the bottom section to the top section, Id suggest color coding since its easy to get lost in the mess
Your 3D wireframe is complete

9th pic
Now for the solids editing part
Create a solid, any will do as long as it completely included the wireframe
Next, slice the solid along each pentagon. 3Dorbit and the shading options help here



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