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What Are Solid Shapes? Three-dimensional Solids

What are solid shapes? Three-dimensional solids

 

Solid shapes are three-dimensional geometric shapes. The main characteristic is that they have three dimensions (height, length, and width) and occupy space.

Drawing Irregular Shapes: One Point...
Drawing Irregular Shapes: One Point Perspective

In general, they are 3D shapes that delimit or describe volumes. The three elements that make up three-dimensional shapes are faces, edges, and vertices.

We can easily understand a geometric solid from various examples. For example, a square is a quadrilateral: a four-sided geometric figure represented on a flat surface. On the other hand, a cube is a polyhedron with six square faces: a geometric solid with height, width, and length.

What Is a Polyhedron?

Polyhedrons are a particular case of solid shapes whose faces are all polygons. Among them, we can distinguish regular polyhedrons and irregular polyhedra

A polyhedron is the equivalent of any polygon in 2D shapes in three-dimensional geometry.

Regular polyhedra are made up of regular polygons. These types of solid shapes can be classified according to the number of faces.

Regular polyhedra are the most symmetrical. There are nine regular polyhedra: five convex polyhedra and four-star polyhedra.

A convex polyhedron is a polyhedron that embeds a convex solid; that is, for each pair of points in the shape, the line segment joining them is wholly contained in the solid body.

The five convex examples have been known since ancient times called Platonic polyhedra. These solids are the triangular pyramid, tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

A Specific Case of Polyhedron: Pyramid Trunk

What are solid shapes? Three-dimensional solidsThe frustum of a pyramid is a polyhedron made up of two parallel bases with the same number of edges. On the other hand, it is composed of trapezoid-shaped lateral faces. The number of faces is the same as the number of edges of the bases.

Pyramid trunks are obtained by sectioning a pyramid with an intermediate plane parallel to its base. The lower part is a truncated pyramid of the two resulting pieces, and the upper part is still a pyramid.

What Are Prisms?

A prism is a polyhedron with two equal flat surfaces in parallel planes. The remaining faces of the prism are parallelograms that have common sides with these polygons. These parallelograms are called the prism's lateral faces, and the remaining two polygons are called the bases.

The base's polygon determines the name of the prism. For example: if the floors are triangles, it is a triangular prism.

Based on the base, these types of solid can be named as:

  • Triangular: Each floor is in the shape of a triangle.

  • Quadrangular: has each of the bases in the form of a quadrilateral.

  • Pentagonal: has each of the floors in the shape of a pentagon.

  • Hexagonal: has each of the bases in the form of a hexagon.

  • Octagonal: has each of the floors in the shape of an octagon.

What Are Solid Round Shapes?

We define round solid shapes as geometric solids with at least one curved face. This solid shape can be obtained by rotating a flat shape around an axis. Therefore, sometimes it receives the name of solid of revolution.

Some examples of solid round shapes are:

  • The sphere is the figure generated by rotating a circle through an axis that passes through the center. In this case, it has a single curved surface and no edges. Also, all points on the surface are equidistant from the center of the sphere.

  • The cone is generated by revolving a right triangle around one of its legs. This figure has a single flat face formed by a circle.

  • The cylinder is formed by rotating a rectangle around one of its sides.

Examples of Geometric Solids in Everyday Life

In real life, we ​​find many objects with shapes of geometric solids. Here are some examples:

  • A soccer ball takes the form of a sphere.

  • The form of the planets of the Solar System.

  • The pyramids of Egypt. 

  • A cone to organize traffic.

  • An ice cream cone.

  • The dices used in various games are cubes.

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Published: January 16, 2022
Last review: January 16, 2022