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Intersection of a cube and cuboid
  Intersected solids

[August 6th 2009] This is a surface developed model of two intersecting cuboids where a cube (l 50mm) is intersected by a cuboid (30mmX30mmX100mm). The intersection is such that the axis of the cube coincides with the major diagonal of the cube. The slideshow below presents the evolution of the design across stages. The complete drawing is presented after the slideshow.

<p><b>Step-1</b> Draw the top and front view of a cube with width 50 mm. Top view is the bottom image and front profile is the above image <p><b>Step-2</b> Rotate the top 45 deg to align its diagonal vertically. Draw the corresponding front profile <p><b>Step-3</b> Rotate the front profile to align its diagonal vertically <p><b>Step-4</b> Deduce the top profile (marked with blue outline) <p><b>Step-5</b> Intersect with the profile of a cuboid with the square face 30mm in width. Note that the top profile will be concentric with the hexagon containing the vertices of the cube top profile <p><b>Step-6</b> Project the bottom face of the cube from the top profile, parallel to its bottom edge. Marked in magenta. <p><b>Step-7</b> Deduce the true lengths from the top and side projections. The lines highlighted in blue represent the true length of the cut surface. This can now be mapped onto the developed surface of a cube <p>A simulated 3d perspective model of the solid <p>A simulated 3d perspective model of the solid with X ray rendering turned on to help visualize the intersection lines <p>The intersected solid has been developed <p>Finished solid <p>Finished solid <p>Finished solid