Archimedean Solid Truncated Tetrahedron
3,6,6
Deck: Isosceles Triangle Deck
Roof Surface Faces: 2 x Isosceles Triangles, 1 x Equilateral Triangle
SS = 29.4962084968°
DD Plan Angle = 56.4426902380°
R1m = 25.2394018209°
P2m = 30.00°
C5m = 15.7931690484°
S = 58.5178458947°
D Plan Angle = 16.7786548810°
R1a = 25.2394018209°
P2a = 60.00°
C5a = 54.7356103172°
Edges 18, 4 triangular and 4 hexagon faces.
Dihedral Angle Between Faces 3,6 = 109.471220635°
Dihedral Angle Between Faces 6,6 = 70.5287793656°
Isosceles Triangle
Develpoment
Circles
Radius = 1.73205080757
D Angle = 16.77865°
S Rafter Angle = 58.51785°
Hip Rafter Length = 1
Isosceles Triangle Deck
P2a Angle = 30.00°
Common
Rafter Run
Hip Rafter Run
D Angle = 16.77865°
Real Roof
Surface
DD Angle = 56.44269°
Common Rafter Length
SS Rafter Angle = 29.49621°
P2m Angle = 60.00°
Radius = 1
Archimedean Solid Truncated Tetrahedron 3,6 Polygon Corner
Tetrahedron Angles
D Angle = 56.4426902380
A Angle = 29.4962084968
C Angle = 25.2394018209
E Angle = 30.0000000000
B Angle = 15.7931690484
90-D Angle = 33.5573097620
90-A Angle = 60.5037915032
90-C Angle = 64.7605981791
90-E Angle = 60.0000000000
90-B Angle = 74.2068309516
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( 29.4962084968° ) * sin( 56.4426902380° )) = 25.2394018209°
Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) )
Hip Rafter Backing Angle = arctan( sin( 25.2394018209°) ÷ tan( 56.4426902380° ) ) = 15.7931690484°
Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle ))
Hip Rafter Side Cut Angle = arctan( cos( 25.2394018209° ) ÷ tan( 56.4426902380° )) = 30.9637565321°
Dihedral Angle = 180° - 15.7931690484 - 54.7356103172° = 109.471220635°
Settings for Cutting Hip Rafter Material On Side of material
Saw Miter Angle = 25.2394018209°
Saw Blade Bevel Angle = 56.4426902380°
Settings for Cutting Hip Rafter Material On Top Edge of material
Top Edge of Hip Rafter Saw Miter Angle = 59.0362434679°
Top Edge of Hip Rafter Saw Blade Bevel Angle = 13.6330222255°
Archimedean Solid Truncated Tetrahedron 6,6 Polygon Corner
Tetrahedron Angles
D Angle = 16.7786548810
A Angle = 58.5178458947
C Angle = 25.2394018207
E Angle = 60.0000000000
B Angle = 54.7356103172
90-D Angle = 73.2213451190
90-A Angle = 31.4821541053
90-C Angle = 64.7605981793
90-E Angle = 30.0000000000
90-B Angle = 35.2643896828
Platonic Solid or Archimedeans Solid Angles for Compound Miter Saw Settings
Platonic Solid or Archimedeans Solid Face = Hexagon
Jack Rafter Side Cut Angle = 60.0000000000°
Hip Rafter Pitch Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle ))
Hip Rafter Pitch Angle = arctan( tan( 58.5178458947° ) * sin( 16.7786548810° )) = 25.2394018207°
Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) )
Hip Rafter Backing Angle = arctan( sin( 25.2394018207°) ÷ tan( 16.7786548810° ) ) = 54.7356103172°
Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle ))
Hip Rafter Side Cut Angle = arctan( cos( 25.2394018207° ) ÷ tan( 16.7786548810° )) = 71.5650511771°
Dihedral Angle = 180° - 54.7356103172° - 54.7356103172° = 70.5287793656°
Settings for Cutting Hip Rafter Material On Side of material
Saw Miter Angle = 25.2394018207°
Saw Blade Bevel Angle = 16.7786548810°
Settings for Cutting Hip Rafter Material On Top Edge of material
Top Edge of Hip Rafter Saw Miter Angle = 18.4349488229°
Top Edge of Hip Rafter Saw Blade Bevel Angle = 24.0948425521°
Archimedean Solid Rhombicuboctahedron
3,4,4,4
Deck: Trapezoid
Roof Surface Faces: 3 x Isosceles Triangle, 1 x Equilateral Triangle
SS = 24.3744169125°
DD Plan Angle = 57.6315871772°
R1m = 20.9410204723°
P2m = 30.00°
C5m = 12.7643896828°
S = 30.3611934049°
D Plan Angle = 40.7894709409°
R1a = 20.9410204723°
P2a = 45.00°
C5a = 22.50°
Edges 48, 8 triangular and 18 square faces.
Dihedral Angle Between Faces 3,4 = 144.735610317°
Dihedral Angle Between Faces 4,4 = 135.00°
Trapezoid
Develpoment
Circles
Radius = 1.414214
Common Rafter Length
Hip Rafter Length = 1
Common
Rafter Run
D Angle = 40.78947°
S Rafter Angle = 30.36120°
Hip Rafter Run
Trapezoid Deck
P2a Angle = 45.00°
D Angle = 40.78947°
Real Roof
Surface
DD Angle = 57.63159°
SS Rafter Angle = 24.37440°
P2m Angle = 30.00°
Radius = 1
Archimedean Solid Rhombicuboctahedron 4,4 Polygon Corner
Tetrahedron Angles
D Angle = 40.7894709409
A Angle = 30.3611934048
C Angle = 20.9410204722
E Angle = 45.0000000000
B Angle = 22.5000000000
90-D Angle = 49.2105290591
90-A Angle = 59.6388065952
90-C Angle = 69.0589795278
90-E Angle = 45.0000000000
90-B Angle = 67.5000000000
Platonic Solid or Archimedeans Solid Angles for Compound Miter Saw Settings
Dihedral Angle = 135.0000000000°
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( 30.3611934048° ) * sin( 40.7894709409° )) = 20.9410204722°
Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) )
Hip Rafter Backing Angle = arctan( sin( 20.9410204722°) ÷ tan( 40.7894709409° ) ) = 22.5000000000°
Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle ))
Hip Rafter Side Cut Angle = arctan( cos( 20.9410204722° ) ÷ tan( 40.7894709409° )) = 47.2657903991°
Dihedral Angle = ( 90° - Hip Rafter Backing Angle ) * 2
Dihedral Angle = ( 90° - 22.5000000000 ) * 2 = 135.0000000000°
Settings for Cutting Hip Rafter Material On Side of material
Saw Miter Angle = 20.9410204722°
Saw Blade Bevel Angle = 40.7894709409°
Settings for Cutting Hip Rafter Material On Top Edge of material
Top Edge of Hip Rafter Saw Miter Angle = 42.7342096009°
Top Edge of Hip Rafter Saw Blade Bevel Angle = 15.6998574050°
Archimedean Solid Rhombicuboctahedron 3,4 Polygon Corner
Tetrahedron Angles
D Angle = 57.6315871772
A Angle = 24.3744169125
C Angle = 20.9410204723
E Angle = 30.0000000000
B Angle = 12.7643896828
90-D Angle = 32.3684128228
90-A Angle = 65.6255830875
90-C Angle = 69.0589795277
90-E Angle = 60.0000000000
90-B Angle = 77.2356103172
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( 24.3744169125° ) * sin( 57.6315871772° )) = 20.9410204723°
Hip Rafter Backing Angle = arctan( sin( Hip Pitch Angle) ÷ tan( Plan Angle ) )
Hip Rafter Backing Angle = arctan( sin( 20.9410204723°) ÷ tan( 57.6315871772° ) ) = 12.7643896828°
Hip Rafter Side Cut Angle = arctan( cos( Hip Rafter Pitch Angle ) ÷ tan( Plan Angle ))
Hip Rafter Side Cut Angle = arctan( cos( 20.9410204723° ) ÷ tan( 57.6315871772° )) = 30.6246821110°
Dihedral Angle = 180° - 12.7643896828 - 22.500 = 144.735610317°
Settings for Cutting Hip Rafter Material On Side of material
Saw Miter Angle = 20.9410204723°
Saw Blade Bevel Angle = 57.6315871772°
Settings for Cutting Hip Rafter Material On Top Edge of material
Top Edge of Hip Rafter Saw Miter Angle = 59.3753178890°
Top Edge of Hip Rafter Saw Blade Bevel Angle = 11.0310955788°