Reciprocal Roof

Billy Dillon thought it would be fun to build a reciprocal roof .  I agreed, and I said I would build a pentagonal reciprocal roof. He wants to build an hexagonal reciprocal roof , because he likes the geometry of an hexagonal roof better and I wanted fewer rafters to cut.

Billy Dillon's Hexagonal reciprocal roof model.

German Schiftzirkel  (Reciprocal ) roofs.

Shift = Shiften
Zirkel = Circle or Compass

Here's a drawing of the geometry for the  typical Mandala Reciprocal Roof with 8 sides(Octagonal).

Here's my Pentagonal Reciprocal Roof  drawing. 

I  need to see if there's a theory on the radius's of the two circles that the rafters are tangent to.  In the octagonal reciprocal roof   their 45 cm and 8 cm. 8÷ 45 = 0.1777 ratio. I don't know if the 0.1777 is a standard ratio for the two radius's. I tried a 45° rafter slope angle for the pentagonal roof, but the seat lines wouldn't connect properly. I readjusted the slope angle to 30° and the seat lines work. I wonder if there's a theory on the roof slope as well.

Use the same geometry for Jack Rafters Plumb To Earth

for the Seat-Claw Angle. This not in any book. This is geometry I developed.  I would also classify the reciprocal roof rafters as Jack Rafters Plumb To The Earth offset/skewed from the plate line. Using the same geometry of Jack Rafters Plumb To Earth draw a line tangent-perpendicular to the reciprocal roof rafter that intersects the extended run line of the opposing  reciprocal roof rafter. Then draw a line to the rise line of the reciprocal roof rafter. The intersection of theses two lines will give you the seat angle of the reciprocal roof rafters.

I drew the back bevel angles the wrong direction on the 2x4 rafter, but reversed the back bevel angle before I cut the rafters.