How does the decomposition into segments/triangles generalize to 3+ dimensions? If you try decomposing a tetrahedron into multiple tetrahedra, you actually get 4 tetrahedra and 1 octahedron, as shown here.
EDIT: answered my own question:
You can decompose an octahedron into 4 tetrahedrons. They’re irregular, but this is actually fine for the purpose of the lemma.
Clarifying question for #9:
How does the decomposition into segments/triangles generalize to 3+ dimensions? If you try decomposing a tetrahedron into multiple tetrahedra, you actually get 4 tetrahedra and 1 octahedron, as shown here.
EDIT: answered my own question:
You can decompose an octahedron into 4 tetrahedrons. They’re irregular, but this is actually fine for the purpose of the lemma.