Uploaded September 2012 | Updated September 2026, 2 weeks ago
The unit that is used forms a dodecahedron with the corners sticking out. Within this dodecahedron the units have the curve of a sphere. However, when squeezing the corners a little and pushing them inward a little, the spheric curve turns into a hyperbolic curve. After doing this, the central pentagons can be removed. This leads to a nice open structure with which a dome can be built of 6 hyperbolic dodecahedra, the result looks more like an icosahedron with holes then like a dodecahedron, but it is built like a dodecahedron. It is different from the Sierpinski dodecahedron, in which all dodecahedra have the same orientation. Instead, it is similar the second layer in the dodecahedron used as a honeycomb in hyperbolic space, in the center a larger hyperbolic dodecahedron fits.
The unit that is used forms a dodecahedron with the corners sticking out. Within this dodecahedron the units have the curve of a sphere. However, when squeezing the corners a little and pushing them inward a little, the spheric curve turns into a hyperbolic curve. After doing this, the central pentagons can be removed. This leads to a nice open structure with which a dome can be built of 6 hyperbolic dodecahedra, the result looks more like an icosahedron with holes then like a dodecahedron, but it is built like a dodecahedron. It is different from the Sierpinski dodecahedron, in which all dodecahedra have the same orientation. Instead, it is similar the second layer in the dodecahedron used as a honeycomb in hyperbolic space, in the center a larger hyperbolic dodecahedron fits.
