Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dihedral angles and orthogonal polyhedra   Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a
suitable rotation) all faces are perpendicular to a coordinate axis, and hence
all edges are parallel to a coordinate axis. Clearly, any facial angle and any
dihedral angle is a multiple of $\pi/2$.
  In this note we explore the converse: if the facial and/or dihedral angles
are all multiples of $\pi /2$, is the polyhedron necessarily orthogonal? The
case of facial angles was answered previously. In this note we show that if
both the facial and dihedral angles are multiples of $\pi /2$ then the
polyhedron is orthogonal (presuming connectivity), and we give examples to show
that the condition for dihedral angles alone does not suffice.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: astro-ph