## Kepler-Poinsot solids
In the great stellated dodecahedron and the small
stellated dodecahedron, the faces are pentagrams (five-pointed
stars). The center of each pentagram is hidden inside the polyhedron. These
two polyhedra were described by Johannes Kepler
in 1619, and he deserves credit for first understanding them mathematically,
though a 16th century drawing by the Nuremberg goldsmith Wentzel Jamnitzer
(1508–1585) is very similar to the former and a 15th century mosaic
attributed to the Florentine artist Paolo Uccello (1397–1475) illustrates
the latter. The great icosahedron and great dodecahedron
were described by Louis Poinsot in 1809,
though Jamnitzer made a picture of the great dodecahedron in 1568. In these
the faces (20 triangles and 12 pentagons, respectively) which meet at each
vertex "go around twice" and intersect each other, in a manner that is the
three-dimensional analog to what happens in two-dimensions with a pentagram.
Together, the Platonic solids and these Kepler-Poinsot polyhedra form the
set of nine regular polyhedra. Augustin Cauchy
first proved that no other polyhedra can exist with identical regular faces
and identical regular vertices. ## Related category• SOLIDS AND SURFACES | |||||||

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