  This work rests upon the certainty that only fields of real and complex
numbers, quaternions and octonions have algebras of all four arithmetical
operations. Also quaternions are good to represent 3-dimensional Euclid space
and 4-dimensional Minkowski space. Moreover algebra of Pauli classical
sigma-matrices isomorphic to a split quaternion algebra. In this article author
supposes that the hyperspace can be described with octonions and if
4-dimensional Minkowski space is a projection of the hyperspace, consequently
equations for 4-dimensional space must be projections of hyperspace equations.
Therefore he obtains a new object as volumetric analog of Pauli sigma-matrices
for 8 (or maybe 24)-dimensional hyperspace. Also the author represents general
form of a volumetric Dirac equation solution. As is well known nonassociativity
is the main distinctive feature of octonions. But square matrices cannot be
nonassociative. Therefore the author had to introduce cubic sigma-matrices.
From another hand a volumetric object has 3 indices, as a result of it one
cannot introduce multiplicative operator for cubic matrices, their projections
only can be objects of the multiplicative operator. Meanwhile an uncertainty
appears because of a rest index. To overcome the uncertainty one need to
consider all the 3 projections of an octonion equation.
