  In the 3-dimensional Berwald-Moor space are bingles and tringles constructed,
as additive characteristic objects associated to couples and triples of unit
vectors - practically lengths and areas on the unit sphere. In analogy with the
spherical angles, we build two types of bingles (reciprocal and relative). It
is shown that reciprocal bingles are norms in the space of exponential angles
(in the bi-space H^{\flat}, which exponentially define the representation of
poly-numbers. It is shown that the metric of this space coincides with the
Berwald-Moor metric of the original space. The relative bingles are connected
to the elements of the second bi-space (angles, in the space of angles)
H^{2\flat} and allow to provide the doble-exponential representation of
poly-numbers. The explicit formulas for relative bingles and tringles contain
integrals, which cannot be expressed by means of elementary functions.
