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1
Geometry of Four Dimensions
Polyhedral sections of a plano-polyhedral angle. Right sections. A hyperplane
intersecting the edge of a plano-polyhedral angle, but not containing the edge,
intersects the faces in half-lines which are the edges of a polyhedral angle; and
the ...
Every convex polyhedral angle is the boundary of the convex hull of its edges
and is therefore uniquely determined by specifying its vertex and the directions of
its edges. (We say that such an angle is spanned by its edges.) Indeed, if a solid
...
N.S. Dairbekov, A.D. Alexandrov, Semën Samsonovich Kutateladze, 2006
3
The Mathematics Dictionary
See POLAR — polar coordinates in the plane. polyhedral angle. The
configuration formed by the lateral faces of a polyhedron which have a common
vertex (A-BCDEF in the figure); the positional relation of a set of planes
determined by a ...
4
Plane and Solid Geometry
The opening of three or more planes which meet at a common point is called a
polyhedral angle. The common point V is called the oertea: of the angle; the
intersections VA, VB, etc., of the planes are called the edges; the portions of the
planes ...
5
A.D. Alexandrov: Selected Works Part II: Intrinsic Geometry ...
Now let us prove our lemma in the case where our cone turns out to be a
polyhedral angle. Let α1 ,α 2 ,...,α n be plane angles of this polyhedral angle. If
we revolve the support plane to the polyhedral angle along one of the edges,
then the end ...
6
Proceedings of the Symposium on Recent Advances in the ...
In the case of a three faces polyhedral angle, three pentagons joined to a central
hexagon can be arranged if in each of the touching triangles vertices, 2'/6
hexagons are eliminated (Fig. 6d). In the case of a four faces angle, an hexagon
with ...
Karl M. Kadish, Rodney S. Ruoff, 1997
7
Handbook of Mathematics for Engineers and Scientists
Two edges belonging to the same face form a face angle of the polyhedral angle,
and two neighboring faces form a dihedral angle. Polyhedral angles are equal (
congruent) if one can be transformed into the other by translations and rotations.
Andrei D. Polyanin, Alexander V. Manzhirov, 2006
8
Geometry, Its Elements and Structure: Second Edition
Definition 13-1 A polyhedral angle is the figure formed by three or more planes
that intersect in one point. The point of intersection of all the planes is called the
vertex of the polyhedral angle. The planes are called faces; the intersections of
the ...
Alfred S. Posamentier, J. Houston Banks, Robert L. Bannister, 2014
A polyhedral angle is the figure generated by a moving straight line segment that
continually intersects the boundary of a fixed polygon and one extremity of which
is a fixed point not in the plane of the given polygon. A polyhedral angle is ...
Clara Avis Hart, Daniel D. Feldman, John Henry Tanner, 1912
10
Extrinsic Geometry of Convex Surfaces
... in the set flP. If 5 is sufficiently small, each vertex Ai (i ^ k) of the polyhedron Q
coincides with the corresponding vertex of the polyhedron Q', and the polyhedral
angle of Q' contains the polyhedral angle of Q. If the polyhedral angle of Q at A, ...
Alekseĭ Vasilʹevich Pogorelov
