Rhombicosidodecahedron
From Wikipedia, the free encyclopedia
is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
Archimedean solid
From Wikipedia, the free encyclopediaIn geometry, an Archimedean solid is a highly symmetric, semi-regular
convex polyhedron composed of two or more types of regular polygons meeting
in identical vertices. They are distinct from the Platonic solids,
which are composed of only one type of polygon meeting in identical vertices,
and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.
Rhombicosidodecahedron Vertex - Deck -- Ground Plan.
Rhombicosidodecahedron Roof Slope Angles with hip rafter offset for roof plane alignment.
Rhombicosidodecahedron Roof Surface Unfolded.
Rhombicosidodecahedron Roof Surface Angles.
Cut Square, Triangle & Pentagon pieces,
then miter sides of Square, Triangle and Pentagon using Hip Rafter Backing Angle.
The same as cutting roof sheathing. The hip rafters will be different sizes and the hip rafters will not be centered on the hip rafter run line.
Rhombicosidodecahedron Roof Sheathing with a SkillSaw
- Cut 2 half square triangles with two legs at 12", the length of the hip rafter and a base leg of 16.97". 45° roof sheathing angles and 45° jack rafter side cut angles on the roof surface. Hip Rafter Backing Angle = Saw Blade bevel Angle = 18.46°
- Cut 1 equilateral triangle with edge lengths of 12". 60° roof sheathing angles and 30° jack rafter side cut angles on the roof surface. Hip Rafter Backing Angle = Saw Blade bevel Angle = 14.98°
- Cut 1 triangle for the pentagon side piece. Two legs at 12" and a base leg of 19 7/16". 36° roof sheathing angles and 54° jack rafter side cut angles on the roof surface. Hip Rafter Backing Angle = Saw Blade bevel Angle = 22.39°
Rhombicosidodecahedron Hip Rafters with equal length miter line plane.
Hip Rafter Miter Angles Hip Rafter Width = 1.00000 Roof Eave Angle for Hip Rafter A = 102.62142 Hip Rafter A Slope Angle = 12.93932 Roof Slope Angle A = 14.98460 Roof Slope Angle B = 18.46161 Plan Angle on Side A = 59.13432 Plan Angle on Side B = 43.48710 Roof Eave Angle for Hip Rafter B = 77.37858 Hip Rafter B Slope Angle = 12.93932 Roof Slope Angle B = 18.46161 Roof Slope Angle C = 22.39277 Plan Angle on Side B = 43.48708 Plan Angle on Side C = 33.89150 Plan Miter Peak Angle = 93.02582 Hip Rafter A Offset Perpendicular = 0.36180 Hip Rafter B Offset Perpendicular = 0.58541 Hip Rafter A Miter Line Peak Plan Angle 1 = 32.53731 Hip Rafter A Miter Line Peak Plan Angle 2 = 57.46269 Hip Rafter B Miter Line Peak Plan Angle 1 = 60.48851 Hip Rafter B Miter Line Peak Plan Angle 2 = 29.51149 Hip Rafter A Miter Line Slope Angle R5P = 10.96195 Hip Rafter B Miter Line Slope Angle R5P = 6.45702 Hip Rafter A R5B = 9.46376 Hip Rafter A R5B = 9.46376 Hip Rafter A - R4P Angle = 31.87278 Hip Rafter B - R4P Angle = 59.85263 Hip Rafter A Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material Laying Flat-- Side Face Hip Rafter A Miter Angle = 12.93932 Hip Rafter A Saw Blade Bevel Angle = 57.46269 Hip Rafter B Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material Laying Flat-- Side Face Hip Rafter B Miter Angle = 12.93932 Hip Rafter B Saw Blade Bevel Angle = 29.51149 Hip Rafter A Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material On Top Edge Hip Rafter A Tetrahedron Angles D Angle = 77.06068 A Angle = 32.53731 C Angle = 31.87278 E Angle = 10.96195 B Angle = 6.91718 90-D Angle = 12.93932 90-A Angle = 57.46269 90-C Angle = 58.12722 90-E Angle = 79.03805 90-B Angle = 83.08282 Saw Miter Angle = 58.12722 Saw Blade Bevel Angle = 6.91718 Bevel Angle (Compound Angle) = 12.93932 Hip Rafter B Compound Miter Angle and Saw Blade Bevel Angle Settings for Cutting Material On Top Edge Hip Rafter B Tetrahedron Angles D Angle = 77.06068 A Angle = 60.48851 C Angle = 59.85263 E Angle = 6.45702 B Angle = 11.23695 90-D Angle = 12.93932 90-A Angle = 29.51149 90-C Angle = 30.14737 90-E Angle = 83.54298 90-B Angle = 78.76305 Saw Miter Angle = 30.14737 Saw Blade Bevel Angle = 11.23695 Bevel Angle (Compound Angle) = 12.93932
Rhombicosidodecahedron Dihedral Angles and Hip Rafter Backing Angles
Angular Dimension (159.09484°)
Dihedral Angle = 159.094842552°
30° - 7.6226318595° ... Hip Rafter Backing Angle
45° - 13.2825255889°... Hip Rafter Backing Angle
Face Angle A = 45.00000 ... Roof Sheathing Angle
Face Angle B = 60.00000 ... Roof Sheathing Angle
Face Angle C = 102.62142 ... Eave Angle
Dihedral Angle A = 14.98459 ...Common/Profile Rafter Slope Angle
Dihedral Angle B = 18.46160...Common/Profile Rafter Slope Angle
Dihedral Angle C = 159.09486
Dihedral Angle = 148.282525587°
45° - 13.2825255889°... Hip Rafter Backing Angle
54° - 18.4349488239°... Hip Rafter Backing Angle
Face Angle A = 45.00000...Roof Sheathing Angle
Face Angle B = 36.00000... Roof Sheathing Angle
Face Angle C = 77.37858... Eave Angle
Dihedral Angle A = 22.39278...Common/Profile Rafter Slope Angle
Dihedral Angle B = 18.46162...Common/Profile Rafter Slope Angle
Dihedral Angle C = 148.28251
Dihedral Angle Formulas
Dihedral angle C = arccos((cos(c) - cos(a) × cos(b)) ÷ (sin(a) × sin(b)))Dihedral angle A = arccos((cos(a) - cos(b) × cos(c)) ÷ (sin(c) × sin(b)))
Dihedral angle B = arccos((cos(b) - cos(a) × cos(c)) ÷ (sin(a) × sin(c)))
Tetrahedron Angles D Angle = 59.1343387352 A Angle = 14.9845972120 C Angle = 12.9393184374 E Angle = 30.0000000000 B Angle = 7.6226318595 90-D Angle = 30.8656612648 90-A Angle = 75.0154027880 90-C Angle = 77.0606815626 90-E Angle = 60.0000000000 90-B Angle = 82.3773681405 Platonic Solid or Archimedeans Solid Angles for Compound Miter Saw Settings Platonic Solid or Archimedeans Solid Face = Equilateral Triangle Jack Rafter Side Cut Angle = 30.0000000000° Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle )) Hip Rafter Pitch Angle = arctan( tan( 14.9845972120° ) * sin( 59.1343387352° )) = 12.9393184374° Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) ) Hip Rafter Backing Angle = arctan( sin( 12.9393184374°) ÷ tan( 59.1343387352° ) ) = 7.6226318595° Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle )) Hip Rafter Side Cut Angle = arctan( cos( 12.9393184374° ) ÷ tan( 59.1343387352° )) = 30.2207003332° Dihedral Angle = 90° - 7.6226318595° - 7.6226318595° = 164.7547362810° Settings for Cutting Hip Rafter Material On Side of material Saw Miter Angle = 12.9393184374° Saw Blade Bevel Angle = 59.1343387352° Settings for Cutting Hip Rafter Material On Top Edge of material Top Edge of Hip Rafter Saw Miter Angle = 59.7792996668° Top Edge of Hip Rafter Saw Blade Bevel Angle = 6.5964995205°
Tetrahedron Angles D Angle = 43.4870777454 A Angle = 18.4616148311 C Angle = 12.9393184374 E Angle = 45.0000000000 B Angle = 13.2825255889 90-D Angle = 46.5129222546 90-A Angle = 71.5383851689 90-C Angle = 77.0606815626 90-E Angle = 45.0000000000 90-B Angle = 76.7174744111 Platonic Solid or Archimedeans Solid Angles for Compound Miter Saw Settings Platonic Solid or Archimedeans Solid Face = Square Jack Rafter Side Cut Angle = 45.0000000000° Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle )) Hip Rafter Pitch Angle = arctan( tan( 18.4616148311° ) * sin( 43.4870777454° )) = 12.9393184374° Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) ) Hip Rafter Backing Angle = arctan( sin( 12.9393184374°) ÷ tan( 43.4870777454° ) ) = 13.2825255889° Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle )) Hip Rafter Side Cut Angle = arctan( cos( 12.9393184374° ) ÷ tan( 43.4870777454° )) = 45.7767018361° Dihedral Angle = 90° - 13.2825255889° - 13.2825255889° = 153.4349488222° Settings for Cutting Hip Rafter Material On Side of material Saw Miter Angle = 12.9393184374° Saw Blade Bevel Angle = 43.4870777454° Settings for Cutting Hip Rafter Material On Top Edge of material Top Edge of Hip Rafter Saw Miter Angle = 44.2232981639° Top Edge of Hip Rafter Saw Blade Bevel Angle = 9.3497035428°Tetrahedron Angles D Angle = 33.8915057735 A Angle = 22.3927709301 C Angle = 12.9393184378 E Angle = 54.0000000000 B Angle = 18.4349488239 90-D Angle = 56.1084942265 90-A Angle = 67.6072290699 90-C Angle = 77.0606815622 90-E Angle = 36.0000000000 90-B Angle = 71.5650511761 Platonic Solid or Archimedeans Solid Angles for Compound Miter Saw Settings Platonic Solid or Archimedeans Solid Face = Pentagon Jack Rafter Side Cut Angle = 54.0000000000° Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle )) Hip Rafter Pitch Angle = arctan( tan( 22.3927709301° ) * sin( 33.8915057735° )) = 12.9393184378° Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) ) Hip Rafter Backing Angle = arctan( sin( 12.9393184378°) ÷ tan( 33.8915057735° ) ) = 18.4349488239° Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle )) Hip Rafter Side Cut Angle = arctan( cos( 12.9393184378° ) ÷ tan( 33.8915057735° )) = 55.4231060666° Dihedral Angle = 90° - 18.4349488239° - 18.4349488239° = 143.1301023522° Settings for Cutting Hip Rafter Material On Side of material Saw Miter Angle = 12.9393184378° Saw Blade Bevel Angle = 33.8915057735° Settings for Cutting Hip Rafter Material On Top Edge of material Top Edge of Hip Rafter Saw Miter Angle = 34.5768939334° Top Edge of Hip Rafter Saw Blade Bevel Angle = 10.7120937647°
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