QUOTE
There is a near-Johnson solid which can be constructed by inscribing regular nonagons inside the eight triangular faces of a regular octahedron, then joining the free edges to the 24 triangles and finally the remaining edges of the triangles to six squares, with one square for each octahedral vertex. It turns out that the triangles are not quite equilateral, making the edges that bound the squares a slightly different length from that of the enneagonal edge.
I've often wondered why those things didn't fit exactly correctly... I always thought it was my poor drawing/cutting skills. Nice to know it wasn't really my fault.
(Jon, please no "Johnson" jokes, OK?
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