Need help with polyhedron...

[SilverTiger]

I have no clue as to how to compute my angles of rotation to make this heptagonal-rhomboid-pentagonal polyhedron.

 

Here is the flat layout:

 

And this is what I'm trying to make:

[shift1313]

i thought about it a little and you need to look at it like triangles and do some trig. You know the length across your square is fixed. and that needs to be the distance between your two regular heptagons. the only issue is this needs to be on plane. I would draw some reference triangles and snap to them and measure angles.

[SilverTiger]

I've tried all sorts of triangles and snapping to them and nothing seems to be working right at all...

[shift1313]

what size are you working with. what are the edges on your square?

[SEANT]

I don't think the second picture is dealing with Regular Heptagons (though they may be equilateral).

 

I'm assuming that those are regular heptagons in the Autocad drawing. It looks to be impossible to array them around a regular pentagon, especially given the clearence required to generate the curve.

[tzframpton]

Doesn't Fucarro have some Lisp program that automatically makes this thing?

[Lazarus]

http://www.cadtutor.net/forum/showthread.php?t=8276

Is this thread related to this sort of things?

Could be helpful

[shift1313]

i would have to agree that the shape is irregular. i had to rotate my panels down 39degrees to get them close, then i snapped to the intersection point to make them align properly. this is a huge arc!!!(actually small).

 

[Strix]

the more I look at that the more Escher-esque it gets!

 

the only observation I can make is that each heptagon touches two squares, two pentagons, and two other heptagons - and that arraying any quantity of heptagons about a central point will require said heptagons to be irregular for them to tile in a circular fashion (across a curved surface or otherwise)

 

Might have to borrow Mr Strix's laptop and have a play with that one

[fuccaro]

Doesn't Fucarro have some Lisp program that automatically makes this thing?

It may be... just I can't remember

[SilverTiger]

i would have to agree that the shape is irregular. i had to rotate my panels down 39degrees to get them close, then i snapped to the intersection point to make them align properly. this is a huge arc!!!(actually small).

 

How in the world did you snap to the intersection point? How did you do that exactly? I had an intersection point too where they overlapped each other, but I couldn't figure out a way to snap to it and rotate it accurately...

[shift1313]

i drew my first heptagon by making a single line then an array, pedit to join it. then i drew a square off one of its sides, array of my heptagon around the center point of the square. then i changed my zaxis vector and rotated each heptagon down 39degrees(3x the angle between them in the xy plane). at that point they had a slight over lap and i was just able to drag the edge to the intersection point. what are your osnap settings?

[SilverTiger]

ok...so you changed the shape; what i need is an exact angle of rotation ( it's somewhere between 37deg and 37.0625deg) or a way to align all three edges so that i don't have to rotate at all, preferably the latter because all divided sums of angles seem to end in a fraction of a seventh, which is always a repeating decimal. The shape itself does not need to be changed. If I had to do an exact rotation, I would be able to rotate the heptagons accurately if I knew the radius of the inscribed sphere.

[shift1313]

thats odd because my angle was 38.5 and 39degrees when i drew a regular heptagon.

[SilverTiger]

Is there a way to align the edges of the two heptagons and the square?

[SEANT]

With regular polygons, I'm getting 37.11050 degrees. Angle was derived from the intersections of two Revolved Solids.

 

As mentioned by shift1313; the curvature is quite intense, and is another indication that Regular Polygons may not work for this hedron.

Hept.dwg

[fuccaro]

In the first image I drew a square and two heptagons. Also I rotated the UCS and converted the heptagons to regions.

We wish to rotate the white heptagon around AB. I drew the circle described by its corner M. The center of the circle is along the line AB, at the same Z coord as M is.

In the same way I drew the magenta circle; that is the trajectory of N while rotating around AC (in the mean time I changed the UCS).

 

Where the two circles meet each other –this is the point we should bring N and M.

I used the Align command: first I selected the red heptagon. As first source point I selected A, and A again as first destination point. As second source point I selected C and C again as second destination point. As third source point I selected the corner N and as third destination point I clicked the intersection of the two circles.

 

 

The same goes for the white heptagon.

Does this help you?

[shift1313]

nice. i have never used the align command, now i know. thanks for the great tip.

[SilverTiger]

Wow. I finally got it. Thanks guys. Now I need to do something else. Is there an autolisp or something that allows you to type fractions into an angle when the decimal is a repeater? I need this angle for the splinecurve: 25-4/5deg. I derived this angle by dividing the total number of axes of rotation into 360. In this case, there are 14 total axes. The long white line represents the last axis. When I calculate 360/14, I get 25-4/5, or 25.71428571~ and it is a repeater. I just wish there were a way to enter a fraction as an angle into AutoCAD.

 

[fuccaro]

Try to enter it a lisp expression. When AutoCAD prompts you for an angle enter

(/ pi 7)

It means "divide PI with 7 -that's the same as "divide 2 times PI to 14"

As you can see, the angle must be entered in Radians.

But as in this case, as in the previous one I think you should use geometrical constructions. If you work with numbers you can end-up with accumulated rounding errors... In this case I would use (again) the ALIGN command. Or ROTATE with Reference option