Polyhedra and polytopes26 of 113
Star polyhedra
Kepler 1619, Poinsot 1809
Let the faces of a regular solid pass through one another, as the sides of a pentagram do, and four more regular polyhedra appear. Kepler found the two stellated dodecahedra and Poinsot the great dodecahedron and great icosahedron. Three of the four are shown, with Kepler’s stella octangula, two tetrahedra set through each other. The golden ratio fixes the length of each spike.
spike edge = φ × core edge, φ = (1 + √5) / 2
On mathcurve.com as Polyèdres de Kepler-Poinsot
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3Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 1430
Small stellated dodecahedron, marble floor inlay
An inlay in the basilica floor showing the small stellated dodecahedron, often dated about 1430, two centuries before Kepler described the solid. The attribution to Uccello is repeated widely and documented thinly.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer agreed, 2026-10-09: The holder's page confirms the inlay shows the small stellated dodecahedron in the Basilica of St. Mark floor, which Kepler described in 1619, and it admits "I have not been able to locate any explanation of the evidence attributing this particular inlay to Uccello or how it is dated to that period", matching the note's point that the attribution is thinly documented. The shape entry credits Kepler with the two stellated dodecahedra, so the link to Star polyhedra holds.
- 1949
Two tetrahedra pierce each other as a stella octangula. One is built over with houses and roads, the other is wild, and Escher wrote that they fit together without knowing about each other.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The shape entry confirms that the stella octangula is "Kepler’s stella octangula, two tetrahedra set through each other", but the work's record gives only title, maker, year and holder. Nothing in the evidence shows that Double Planetoid has this form, that one body carries houses and roads while the other is wild, or that Escher wrote about the two fitting together unaware of each other.
- 1952
A small stellated dodecahedron with a creature caught in each of its twelve star points, neck and legs pushed out through the openings.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer agreed, 2026-10-09: The holder's page states "The planetoid featured in Gravity is a small stellated dodecahedron." It adds that each of the 12 stars is a prison for a monster whose neck and paws protrude, which matches the note. The small stellated dodecahedron is one of the Kepler stellated dodecahedra named in the library's star polyhedra entry.