You have to learn to turn and shift the face of the hexahedron
The hexahedral problem type in graphical reasoning has made many children's shoes helpless and prohibitive. It was clear that he had learned various magic skills, but even when he saw the problem, he would still be sluggish and full of doubts. What the hell is going on here? The special face is gone; the relative face cannot exclude options; the adjacent faces are not together; the hour-clock method is invalid; the arrow method has no place to draw arrows; the common edge and the common point cannot be put together... Isn't this a martial art that can't be used in the air? In the end, it is not understood, all the techniques are based on the ability to flexibly analyze the relationship between known surfaces, and analyzing the relationship between known surfaces requires understanding some rules between the three-dimensional surface and the unfolded surface.
Hexahedron, as the name suggests, there are a total of 6 faces, respectively, with A, B, C, D, E, F representing 6 faces, suppose we want to analyze the relationship between A plane and other planes, in 6 faces, in addition to A itself, there are 5 faces will have a relationship with it, 1 of these 5 and it is a relative surface without a common side, and the remaining 4 are all with A side has a common side, that is, we say adjacent planes, assuming that B side is the opposite side of A side, then C, D, E, F These four faces and A are adjacent to each other with common edges. Any face will have four sides, and the A side will naturally have four sides, but which of the four adjacent faces of the A side correspond to each of the four adjacent faces? Only by completely solving this problem can the methods and techniques learned be truly useful, and to solve this problem, we must learn to reasonably move or turn the surface of the face in the hexahedron, so as to determine which side corresponds to which side, which side.
1. Move the surface
Moving surfaces refers to the two surfaces that originally have common edges that can be adjacent, but are separated, and are directly spliced together by translation.
Face shift rule: In the hexahedral unfolding diagram, when there are 4 faces in the same row or the same column, the two sides must be the same common side, and the two faces at both ends can be flattened by translating each other.
Example of moving surfaces: Figure (1) in the figure below belongs to the 4 faces discharged in the same column, the red lines at the upper and lower ends represent the common edges that can be coincident, while figure (2) is the morphology after the reasonable displacement of the surfaces; Figure (3) belongs to the 4 faces of the same row, the red lines at the left and right ends represent the common edges that can be coincident, and figure (4) is the form after the reasonable transfer of the surfaces.
When to use: When there is no one-to-one correspondence between adjacent faces and the adjacent relationship of the original image in the options to be analyzed, and there are 4 faces in the same or same column in the options.
Note the tip: four faces on a line, the end and end of the edge are overlapping edges, overlapping edges, and movable faces.
2. Turn the surface
Turning surfaces refer to the rotation of surfaces that originally have common edges that can be adjacent, but are separated and arranged together by rotation.
Turning surface rule: In the hexahedral unfolding diagram, when the two faces are satisfied with a right angle, the two sides corresponding to the right angle must be the same common side, and the two faces can be spun together by rotation.
Example of a turning face: the angle between the four-colored square face and the yellow face in figure (1) below constitutes a right angle, the red line represents the right angle edge, representing the common edge that can be coincident, figure (2) is the form after reasonable rotation; the angle between the four-color square face and the purple face in figure (3) constitutes a right angle, the red line represents the right angle edge, representing the common side that can be coincident, and figure (4) is the form after reasonable rotation. There are two points to pay attention to when turning a surface, one is that the direction to which a certain surface is going is consistent with the direction of its own rotation; the other is that the degree of rotation is 90°.
When to use: When the options you want to analyze do not correspond to the adjacent relationships of the original image one-to-one between the adjacent polygons.
Remember the tip: the angle between the faces is a right angle, and the right angle side is drawn with "L", not enough to rotate itself two or three times at a time.
Finally, the coastline should remind everyone that although the hexahedron method and technique are relatively obscure, as long as you practice a little on the basis of understanding, the hexahedral question type is a question type that must be scored.