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tet — A single tetrahedron in a triangulation
Content Model | |
tet ::= (#PCDATA) | |
Attributes | |
Name | Type |
desc | CDATA |
A tet
element stores a single tetrahedron in a 3-manifold
triangulation with its associated face gluings.
The character data of this XML element should be a
whitespace-separated list of four integer pairs, representing the
gluings of faces 0, 1, 2 and 3 of this tetrahedron. Note that
face i
is always opposite vertex
i
in a tetrahedron.
For each pair, the first integer represents the tetrahedron to which the face is glued (note that tetrahedra in a triangulation are numbered 0, 1, 2, etc.). The second integer represents the permutation of vertices from this tetrahedron to the other describing precisely how this gluing takes place. This permutation will take the current face number to the corresponding face number of the adjacent tetrahedron, and the other three vertex numbers to the corresponding three vertex numbers on the adjacent tetrahedron to which they are identified by this gluing.
A permutation is represented as a one-byte integer as follows.
If the permutation maps 0, 1, 2 and 3 to
a
, b
,
c
and d
respectively (where
a
, b
,
c
and d
are
0, 1, 2 and 3 in some order), the corresponding one-byte integer
is
(