Abraham Sharp's
Geometry Improv'd

George Hart




In 1717, Abraham Sharp published an unusual little book which describes twelve original polyhedra.  The first and simplest of his new "solid bodies" is an eighteen-sided form that I call the "Sharpohedron".  It consists of six rhombi and twelve kite-shaped faces. Here are four versions of it: solid wood, paper, assembled wood, and 3D-printed. 



To make a paper or wood version, the following face templates and net can be printed, cut out, and taped together. To make a 3D-printed version, use this STL file.



This video explains a bit about it:



I have written a paper about Abraham Sharp, Geometry Improv'd, and the Sharpohedron:

   George Hart, "The Multifaceted Abraham Sharp", in Imagine Math 8: Dreaming Venice, Michele Emmer and Marco Abate (editors), Springer, 2022, pp. 267-294. My final draft of the paper before publication is available here.