Twisted Pyramid

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A regular pyramid is the result of connecting a regular polygon with an apex point directly above the center of the polygon. If you twist a regular pyramid, its lateral faces are no longer triangles but curved surfaces.


This Demonstration shows the effect of axial twisting on the edges and lateral faces of a regular pyramid. A section between the polygonal base and the apex shows the twisted edges and offers an inside view into the twisted pyramid.


Contributed by: Erik Mahieu (March 2015)
Open content licensed under CC BY-NC-SA



A regular -gon has polar equation , where is the radius of the circumcircle, is the number of sides, is the angular offset, and is the polar angle.

Based on this, a regular -gonal prism has the parametric equation , with parameters and .

To get an -gonal pyramid, replace the circumradius in by , where is the height of the pyramid.

To twist the pyramid, replace the angular offset by , where is the total axial twist over the height of the pyramid.

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