How can you cut an octagon with a plane to cut a hexagonal prism?

At most, you can cut out a heptagon, which intersects five of the edges and intersects the base, exactly seven intersections.

On the two adjacent edges AB and FA on the bottom surface, take one point M, N, cross the point M and the point N, and truncate the plane of the other side edges except AA, and truncate the hexagonal prism.

into a heptagon. On the two adjacent edges AB and FA on the bottom surface, take one point of M and N each.

Prismatic **.

The bottom surface is regular hexagonal.

And the 1653 edges on the six sides are perpendicular to the bottom surface.

Prism: Two faces parallel to each other, the rest of the faces are quadrilateral.

And the common edges of each of the two adjacent quadrilaterals are parallel to each other, and the geometry enclosed by these faces is called a prism.

The underside of the prism: The two faces in the prism that are parallel to each other are called the base of the prism, referred to as the bottom.

Sides of the prism: the remaining sides (except the underside of the prism).

We know that the intersection of faces produces lines, and when a hexagonal prism is cut with a plane (i.e., a knife), each face cut will produce a line segment, so in order to get an octagon, you must cut to eight faces. Whereas, the hexagonal prism has exactly two undersides and six sides. In other words, you have to cut all eight faces at the same time to make the section octagonal.

Truncate two corners to create an octagon.

Hexagon, a type of polygon, refers to all polygons with six sides and six corners. According to the regular polygon inner angle and the formula s=180°· (n-2), the sum of the inner angles of all regular hexagons is 720°, and the sum of the outer angles is 360° In nature, the molecular structure of benzene and graphite, turtle shells, honeycomves, etc. are all in the shape of regular hexagons.

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1. Be good at thinking when learning mathematics, and the answers you come up with are far more impressive than the answers told by others.

2. Do a good job of preview before class, so that you can better digest and absorb the knowledge points when you take math class.

3. Mathematical formulas must be memorized, and they must be able to derive and draw inferences.

4. The most basic thing to learn mathematics well is to master the knowledge points of the textbook and the exercises after class.

5. 80% of the scores in mathematics are in the basic knowledge, and 20% of the scores are difficult, so it is not difficult to score 120 points.

Place the triangular prism. It only takes one step to cut out the pentagon:

Use a plane to cut off one corner on the three corners at one end of the triangular prism, and do not cut off the remaining two corners, and the resulting plane is a pentagon. The details are shown in the following figure:

It can be cut out of the comma family code heptagon, and the eight mountains spike source edge.

1. Truncation of heptagons:

The hexagonal prism is obliquely truncated on the negative surface of the flat leakage cover, and is cut out from one end face, so that there is one edge on the end face, and each side has one edge respectively, a total of 7 sides;

2. Truncation of the octagon:

The plane obliquely truncates the hexagonal prism, which is cut out from the two end faces respectively, so that there is an edge on each of the two end faces, and each side has a return strip edge finger, a total of 8 edges.

The shape of the section may be hexagonal, quadrilateral, triangular.

The shape of the section is hexagonal:

<>3. The specific cross-section is as follows.

The shape of the section is quadrilateral:

<>3. The specific cross-section is as follows.

The shape of the section demolition tour is quadrilateral:

<>3. The specific cross-section is as follows.

A pentagonal prism has seven faces, and the section does not intersect at least one of the other faces, so the hexagon with the largest number of sides.

Use a plane to cut a pentagoprism, the section has up to 7 edges, and it needs to be cut from the upper bottom surface obliquely to the side and the lower bottom surface, so that the section will intersect with the 7 faces of the pentagonal prism, and the intersecting edges are 7 edges.

The pentagonal prism has two bottom surfaces, upper and lower, and 5 sides, so there are 7 sides in total. When a geometry is truncated by a plane, the resulting cross-section is a figure enclosed by the intersection of the plane and each face of the geometry. The cross-section of a pentagonal prism can intersect up to 7 faces, so there are up to 7 edges.

The heptagon is truncated from one corner above the pentagonal prism to another corner at the base.

This is the plane that intersects all 7 faces of the pentagonal prism.

OK! Let the hexagonal prism be abcdef-a1b1c1d1e1f1

Three deformations ghi, g coincident a, h coincident c, i on the disadvantage of BB1.

The quadrilateral ghij, g coincident a, h coincident d, i on cc1, j on bb1.

The pentagonal ghijk, g coincident a, h coincident e, i on dd1, j on cc1, k on bb1.

The hexagonal ghijkl, g coincident a, h coincident f, i on ee1, j on dd1, k on cc1, l on bb1.

Seven deformations Ghijklm, G on AB, H on BC, I on Kikura CC1, J on DD1, K on EE1, L on FF1, M on AA1.

The octagon ghijklmn, g on ab, h on bc, i on cc1, j on dd1, k on d1e1, l on e1f1, m on ff1, n on aa1.