Correct polyhedra. Part 2.5 (auxiliary)

In a two-dimensional space, two one-dimensional segments have a common point; the relative position of such segments is determined by an ordinary 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 a 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.
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In four-dimensional space, two three-dimensional polyhedra have a common two-dimensional face, the relative position of such polyhedrons is determined by a three-sided 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 three-sided angle varies from 0 to 360 degrees.
Etc. in N dimensional space, N-1 dimensional polyhedra can have a common N-2 dimensional facet, then the relative position of N-1 dimensional polyhedra is determined by an angle from 0 to 360 degrees.

Under the triangular angle, I understand not what is written in Wikipedia, but the prefix "three" means three-dimensional faces, between which the angle is measured in four-dimensional space. The first two videos are our empirical experience, these turns are obvious to everyone, please focus on the third clip, 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.

Just as in three dimensions, two planes intersect in a straight line and form a dihedral angle in it, in four dimensions two three-dimensional spaces intersect in a plane and in it form a three-sided 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 the 3-roll. On the video, these 3-dimensional spaces are represented by 3-dimensional polyhedra.

I will show how to find these angles between the faces of regular polyhedra in all finite-dimensional spaces. In this article I tried to give a figurative understanding of what we measure and calculate.
What is there to understand? Ask.

Correct polyhedra. Part 1. Trimerie
Correct polyhedra. Part 2. Foursome
Correct polyhedra. Part 2.5 (auxiliary)
Schläfli symbol. Part 2.6