Stefan Röttger

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1) Triangle Case

$P_0$ is cusp end over triangle:

$d_0<0$ and $d_1>0, d2>0, d3>0$
$d_0>0$ and $d_1<0, d2<0, d3<0$
→ $P_{01}, P_{02}, P_{03}$

Decomposes tetrahedron $P_0, P_1, P_2, P_3$ into tetrahedron $P_0, P_{01}, P_{02}, P_{03}$ und prism $P_{01}, P_{02}, P_{03}, P_1, P_2, P_3$

Analogue for cusp ends $P_1, P_2, P_3$

2) Quad Case

$P_0P_1$ is cusp line over quad:

$d_0<0, d_1<0$ and $d2>0, d3>0$
$d_0>0, d_1>0$ and $d2<0, d3<0$

Decomposes tetrahedron $P_0, P_1, P_2, P_3$ into prism $P_0, P_{02}, P_{03}, P_1, P_{12}, P_{13}$ and prism $P_2, P_{02}, P_{12}, P_3, P_{03}, P_{13}$

Analogue for cusp lines $P_0P_2, P_0P_3$

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