The solid is a regular dodecahedron augmented with a pentagonal pyramid on each face. The height of the pyramids can be adjusted so that the triangles are equilateral, but that makes the edges between pentagonal pyramids concave. On Mon, Mar 11, 2019 at 3:47 PM Tom Karzes <karzes@sonic.net> wrote:
Here's a colored, auto-rotating rendering. You can also click- and-drag to manually rotate it (requires a mouse, not a touch screen):
http://www.karzes.com/polyhedra/polyhedron.html?ph=v5.6.6
Tom
Tom Karzes writes:
It looks like the tumble problem has been fixed. Rotating it makes it clear that the triangles are not regular. Wikipedia says they are isosceles, and that the Pentakis Dodecahedron is a Catalan Solid.
Tom
Tom Karzes writes:
I see 6 triangles meeting at a vertex. If the triangles are regular, then either they are coplanar or the polyhedron is concave.
Tom
Bill Gosper writes:
Johnson 93? < https://www.wolframcloud.com/objects/810fbe92-6ab3-480b-9f86-e4869990cf46> —rwg And why can't we tumble that figure?
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