Hyperbolic Pascal Simplex

Authors : László Németh

Pages : 46-55

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Publication Date : 2017-10-29

Article Type : Research Paper

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 whose 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.
Keywords : Hiperbolic Pascal triangle, Pascal simplex, hypercube honeycomb, regular hypercube mosaic in 4 dimensional hyperbolic space, recurrence sequence