Frank Chesters Chestahedron.
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http://www.frankchester.com/2010/chestahedron-geometry/
A volume enclosed by seven sides
...Show more of equal area, made up of four triangles and three quadrilaterals.
The Chestahedron is the first heptahedron of this configuration in the history of geometry. This sculpture has 7 surfaces (consisting of 4 triangles and 3 quadrilaterals), 7 points and 12 edges. If this heptahedron is rotated around the vertical axis, it forms a bell-like external surface of a certain profile: a cone at the top connected to a hyperbolic at the bottom.
