Regular polyhedrons. Part 2.5 (auxiliary)

In two-dimensional space, two one-dimensional segments have a common point, the relative position of such segments is determined by the usual angle. The video shows the rotation of one segment around a common point, while the angle varies from 0 to 360 degrees.



In three-dimensional space, two two-dimensional polygons have a common edge, the relative position of such polygons is determined by the dihedral angle, i.e. angle between two-dimensional faces. The video shows the rotation of one face around a common edge, while the dihedral angle varies from 0 to 360 degrees.



In four-dimensional space, two three-dimensional polyhedra have a common two-dimensional face, the relative position of such polyhedra is determined by the trihedral angle, i.e. angle between three-dimensional faces. The video shows the rotation of one three-dimensional polyhedron around a common two-dimensional face, while the trihedral angle varies from 0 to 360 degrees.
Etc. in N dimensional space, N-1 dimensional polyhedra can have a common N-2 dimensional face, then the relative position of N-1 dimensional polyhedrons is determined by an angle from 0 to 360 degrees.

By a three-sided angle, I understand not what is written on Wikipedia, but the prefix “three” means three-dimensional faces, between which the angle in four-dimensional space is measured. The first two videos are our empirical experience, these turns are obvious to everyone, I ask you to focus on the third roller, where an attempt is made to show the turns of three-dimensional polyhedra around a plane in four-dimensional space, the plane is represented by a triangle, a common two-dimensional face.

As in three-dimensionality, two planes intersect in a straight line and in it form a dihedral angle, - in four-dimensionality two three-dimensional spaces intersect in a plane and in it form a trihedral angle. Similarly, these three-dimensional spaces can rotate around a plane, while the angle between these spaces will vary from 0 to 360 degrees, as I tried to demonstrate on 3 roller. On a roller, these 3 dimensional spaces are represented by 3 dimensional polyhedra.

These angles between the faces of regular polyhedra in all finite-dimensional spaces I will show how to find. In this article I tried to give a figurative understanding of what we measure and calculate.
What is not clear here? Ask.

Regular polyhedrons. Part 1. Three-dimensional
Regular polyhedrons. Part 2. Four-dimensional
regular polyhedrons. Part 2.5 (auxiliary)
The symbol Shafly. Part 2.6