Title: Hyperbolic Pascal simplex,
Abstract: In this article we introduce a new geometric object called hyperbolic Pascal
simplex. This new object is presented by the regular hypercube mosaic in the
4-dimensional hyperbolic space. The definition of the hyperbolic Pascal
simplex, whose hyperfaces are hyperbolic Pascal pyramids and faces are
hyperbolic Pascals triangles, is a natural generalization of the definition of
the hyperbolic Pascal triangle and pyramid. We describe the growing of the
hyperbolic Pascal simplex considering the numbers and the values of the
elements. Further figures illustrate the stepping from a level to the next one.