Images of 3D Model ... Right Triangles composing the Tetrahedra
modeling the Hip Rafter Side Cut Angles at the Peak of the Hip Roof

Main Slope = 10/12     Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90


Development of Tetrahedron modeling the 10/12 Side Angles
(Trigonometric Scale)
Development of Tetrahedron modeling the 10/12 Side Angles

Development of Tetrahedron modeling the 7/12 Side Angles
(Trigonometric Scale)
Development of Tetrahedron modeling the 7/12 Side Angles

Plan View Lines and Angles
Plan View Lines and Angles

Views of the Tetrahedra modeling the Hip Side Cut Angles
juxtaposed along the Triangle of the Hip Slope


Hip Side Cut Angles at Peak of Hip Rafter
Juxtaposed Tetrahedra viewed from
Triangles representing upper shoulder of unbacked Hip Rafter

The triangles follow the plane of the upper shoulder of an unbacked Hip Rafter. This plane passes through a line perpendicular to the Hip Run, and the slope of the plane, measured from level, is equal to 25.54245, the Hip Slope Angle. In other words, the Dihedral Angle between the plane containing the Hip Side Cut Angles and the plane following level is the Hip Slope Angle.
Hip Side Cut Angles at Peak of Hip Rafter ... Juxtaposed Tetrahedra viewed from Triangles representing upper shoulder of unbacked Hip Rafter

Juxtaposed Hip Side Cut Tetrahedra viewed from 10/12 Side
Juxtaposed Hip Side Cut Tetrahedra viewed from 10/12 Side

Juxtaposed Hip Side Cut Tetrahedra viewed from 7/12 Side
Juxtaposed Hip Side Cut Tetrahedra viewed from 7/12 Side

Juxtaposed Hip Side Cut Tetrahedra viewed from the line of the Rise
Juxtaposed Hip Side Cut Tetrahedra viewed from the line of the Rise

Views of the Tetrahedra modeling the Hip Side Cut Angles
separated along the Triangle of the Hip Slope


Oblique View of Hip Side Cut Tetrahedra
Oblique View of Hip Side Cut Tetrahedra

View of Hip Side Cut Tetrahedra from the Triangles of the Hip Slope
View of Hip Side Cut Tetrahedra from the Triangles of the Hip Slope


Cutting the Backing Angle and comparing 3D Geometry Notes ...
Images of Right Triangles composing the Tetrahedra extracted from the Hip Roof
A Study of the Jack Rafter Side Cut Angles


Developments of Tetrahedra extracted from the Hip Roof
Developments of Tetrahedra extracted from the Hip Roof

Views of the Tetrahedra extracted from the Hip Roof
juxtaposed along the Triangle of the Hip Slope


Bird's Eye view of juxtaposed Tetrahedra extracted from the Hip Roof
Jack Rafter Side Cut Triangles about centerline of Backed Hip Rafter

Bird's Eye view of juxtaposed Tetrahedra extracted from the Hip Roof ... Jack Rafter Side Cut Triangles about line of Backed Hip Rafter

Oblique view of juxtaposed Tetrahedra extracted from the Hip Roof
Jack Rafter Side Cut Triangles about centerline of Backed Hip Rafter

Oblique view of juxtaposed Tetrahedra extracted from the Hip Roof ... Jack Rafter Side Cut Triangles about line of Backed Hip Rafter

Oblique view of juxtaposed Tetrahedra extracted from the Hip Roof showing the
hypotenuses of the Hip Side Cut Triangles (unbacked upper shoulder of Hip Rafter)

Oblique view of juxtaposed Tetrahedra extracted from the Hip Roof showing the lines of the Hip Side Cut Triangles (unbacked upper shoulder of Hip Rafter)

Comparison of juxtaposed Hip Rafter Side Cut Angle Tetrahedra (left)
and juxtaposed Tetrahedra modeling the Jack Rafter Side Cut Angles (right)

Comparison of juxtaposed Hip Rafter Side Cut Angle Tetrahedra (left) and juxtaposed Tetrahedra modeling the Jack Rafter Side Cut Angles (right)

Juxtaposed Tetrahedra extracted from the Hip Roof
View from side of the 10/12 Common Slope Triangle

View from side of the 10/12 Common Slope Triangle ... juxtaposed Tetrahedra extracted from the Hip Roof

Juxtaposed Tetrahedra extracted from the Hip Roof
View from side of the 7/12 Common Slope Triangle

View from side of the 7/12 Common Slope Triangle ... juxtaposed Tetrahedra extracted from the Hip Roof

Juxtaposed Tetrahedra extracted from the Hip Roof
View from the line of the Rise

View from the line of the Rise ... juxtaposed Tetrahedra extracted from the Hip Roof

Views of the Tetrahedra extracted from the Hip Roof
separated along the Triangle of the Hip Slope


Oblique view of 10/12 Roof Surface ... Jack Rafter Side Cut Angle
Tetrahedra separated along the Triangle of the Hip Slope: Oblique view of 10/12 Roof Surface ... 10/12 Roof Jack Rafter Side Cut Angle

Oblique view of 7/12 Roof Surface ... Jack Rafter Side Cut Angle
Tetrahedra separated along the Triangle of the Hip Slope: Oblique view of 10/12 Roof Surface ... 7/12 Roof Jack Rafter Side Cut Angle

Tetrahedra extracted from the Hip Roof
viewed from the Triangles of the Hip Slope

Tetrahedra extracted from the Hip Roof viewed from the Triangles of the Hip Slope

Joe Bartok