How to prove there are exactly eight convex deltahedra?
A deltahedron is a polyhedron whose faces are equilateral triangles. It is well-known that there are exactly eight convex deltahedra, and it is easy to find out that this was first proved by Freudenthal and van der Waerden in 1947.
Are equilateral polyhedra with triangular faces rigid?
2022年6月17日 · As noted in a comment, a polyhedron with congruent equilateral triangles for faces is called a "deltahedron". This reference lists "Bellows deltahedra" as flexible deltahedra that seem to meet OP's criteria. It shows two distinct examples, and also links to another (possibly semi-defunct) website with additional images and descriptions of these ...
Counting deltahedra with $2n$ faces - Mathematics Stack Exchange
2020年2月7日 · A deltahedron is, according to Wikipedia, a polyhedron whose faces are all equilateral triangles. There is only one deltahedron with four faces: the tetrahedron. Likewise, there is only one deltahedron with six faces: the triangular bipyramid. There are two with eight faces: the octahedron; the biaugmented tetrahedron (not convex)
Which convex deltahedra are inscribable in the sphere?
2020年10月7日 · A convex deltahedron in $\mathbb{R}^3$ is a convex polyhedron whose faces are all equilateral triangles. There exist precisely 8 convex deltahedra. There exist precisely 8 convex deltahedra. Some examples are the regular tetrahedron, the regular octahedron, and the regular icosahedron.
What's the collective term for the concepts of truncation ...
2018年6月17日 · I recently watched a video on a youtube channel "DONG" led by Michael from Vsauce titled "Making every strictly convex deltahedron" Some concepts like elongation, gyroelongation, expansion, snubification were introduced. I also found concepts like truncation, rectification, and others, on Wolfram MathWorld.
The Dihedral Angles of a Tetrahedron in terms of its edge lengths
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Degree of face of icosahedron is - Mathematics Stack Exchange
2022年3月24日 · My argument below shows that the faces are triangles, making the answer a deltahedron. However the only (convex) deltahedron with 20 faces is an icosahedron. (I am not sure about the non-convex case.) $\endgroup$ –
What polyhedron has 11 vertices and 17 edges
2015年2月4日 · On my math test it asked me how many polygons it takes to create a polyhedron that has $11$ vertices and $17$ edges.
Algorithm for checking if a polyhedron is bounded.
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Is Paley-13 graph a unit distance graph in 3D space?
The 13-node Paley graph has vertices 1 to 13 that are connected by an edge when their difference is one of the values $(1,3,4,9,10,12)$ Can this graph be put into 3D space so that all edges have