Tangent Handrailing Planes and Angles

of this tetrahedron has a vital role to play and will make an appearance later.

Lower Tangent Plane Slope Angle = r5P = 50°

Lower Tangent Plane Plan Angle = dd = 76.73958°

Angle produced on Oblique Plane by trace

of Lower Tangent Plane = r4P = 8.47866°

Dihedral Angle measured between the

Level (Plan View) Plane and the Oblique Plane = R1 = 50.76055°

Dihedral Angle measured between the

Lower Tangent Plane and the Oblique Plane = 90° – a5P = 79.76680°

Upper Tangent Plane Slope Angle = R5P = 40°

Upper Tangent Plane Plan Angle = DD = 43.26042°

Angle produced on Oblique Plane by trace

of Upper Tangent Plane = R4P = 33.90856°

Dihedral Angle measured between the

Level (Plan View) Plane and the Oblique Plane = R1 = 50.76055°

Dihedral Angle measured between the

Upper Tangent Plane and the Oblique Plane = 90° – A5P = 55.66480°

Vertex of the Oblique Plane Triangle ... Angle R4P = 33.90856°

Angle R1 = 50.76055° on the Section Plane is the dihedral angle

measured between the Plan View (Level) Plane and the Oblique Plane.

juxtaposed along their respective Section Planes

down

Angle K P T1 is the "Angle between Tangents"; the angle

produced on the oblique plane by the traces of the tangent planes

= 180° – (r4P + R4P) = 180° – (8.47866° + 33.90856°) = 137.61278°.

Note that the dihedral angle measured between the lower

tangent plane and the oblique plane is 90° + a5P = 100.23320°.

of the upper tangent plane tetrahedron to produce the pentahedron above.

The tetrahedra are shown sitting on the construction of the twist angles

(the dihedral angles measured between the oblique plane and the tangent planes).

points TP and CC, and a plumb plane through points T1 and CC.

As in the pentahedron, the dihedral angle measured between the

lower tangent plane and the oblique plane is 90° + a5P = 100.23320°.

(T2 is the second Point of Tangency on Oblique Plane)

These dihedral angles are the twist angles seen on the handrailing layout on the end grain of the block.

All of the solids above are found in the developed drawing and describe the same group of planes.

... it's always the same surface, angled at 50.76055° with respect to level.