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<glossentry id="angles-tautonly">
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<glossterm><guilabel>Taut structures only</guilabel></glossterm>
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<glossterm><guilabel>Taut angle structures only</guilabel></glossterm>
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If unchecked (the default), ®ina; will enumerate all vertex
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If checked, ®ina; will only enumerate
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<emphasis>taut structures</emphasis>.
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<emphasis>taut angle structures</emphasis>.
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These are angle strutures in which every angle is either 0 or π.
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There are only ever finitely many taut structures (possibly
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none at all), and if you check this box then ®ina; will enumerate
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Note that we use the Kang-Rubinstein definition of taut angle
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structure <xref linkend="bib-kang-taut"/>,
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which is based on the angles alone. We do not use Lackenby's
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definition <xref linkend="bib-lackenby-taut"/>,
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which also requires consistent coorientations on the 2-faces of
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<glossentry id="angles-proptaut">
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<glossterm><guilabel>Taut</guilabel></glossterm>
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Indicates a taut angle structure (all of its angles are
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equal to either 0 or π).
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Indicates a taut angle structure (all of its angles are
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equal to either 0 or π).
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Here we use the Kang-Rubinstein definition of taut angle
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structure <xref linkend="bib-kang-taut"/>,
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which is based on the angles alone. We do not use Lackenby's
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definition <xref linkend="bib-lackenby-taut"/>,
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which also requires consistent coorientations on the 2-faces of
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Note that some taut structures may be listed as
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<link linkend="angles-propveering">veering</link> instead
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(which indicates a stronger combinatorial structure).
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<glossentry id="angles-propveering">
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<glossterm><guilabel>Veering</guilabel></glossterm>
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Indicates a veering structure.
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This is a taut structure with additional (and very strong)
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combinatorial constraints; for details see
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<xref linkend="bib-hodgson-veering"/>.
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Note that we use the Hodgson et al. definition
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of veering structure <xref linkend="bib-hodgson-veering"/>.
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This is slightly more general than Agol's original definition
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<xref linkend="bib-agol-ideal"/>, in the same sense that
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the Kang-Rubinstein definition of taut angle structure is
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slightly more general than Lackenby's. In particular, we do not
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require consistent coorientations on the 2-faces of the triangulation.
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If an angle structure is neither strict nor taut, the
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removed
qtui/doc/regina/angles.docbook
