I need to find the bevel angle of a "box" with 4, 5, 6 or 8 sides. The shape is tilting outward at 10 and 20 degrees. All sides are the same length, and the bevel angle should be the same for each. How would I go about computing this?
Assuming the tilt angle looks something like this: http://jansson.us/planterboxes.jpg Would the tilt angle effect the bevel angle of the box?
My first idea is that since it is box with an overall shape with a standard side length, I could simply solve with a simple equation like this:
360 degrees/number of sides
Would this method work?
The tilt and bevel angle values are the same for a thick rectangular central cross section of planter wall. We can choose either bevel $ { 10^ {\circ}}$ or bevel $ {20^{\circ}}$ ( Angle between horizontal plane and slant face normal) and we have $8$ combinations for polygon frustums $ (p,4,8),$ among which you don't want $(p=7).$
We could have a common base inner circle diameter 1 meter for a set of planter boxes. Image for planter box $ (bevel\,20^{\circ} , p=8 )$ is given:
Top and bottom regular polygons have equal side lengths inside circum diameters $D_1,D_2$ with slant lengths $L,$ so bevel angle can be found from:
$$ \sin(bevel\, angle) =\dfrac{(D_2-D_1) }{2L} $$