Objects that take up space are referred to as "solid forms." Their surfaces are referred to as faces. Faces intersect at edges, and edges intersect at vertices. /span> Vertices are the points where edges of **a polyhedron meet**. Edges can be thought of as branches coming off a vertex, or as the lines that connect **two adjacent vertices**. Faces can be thought of as **the positive shapes** formed by connecting edges that meet at a vertex.

Faces and edges cannot overlap; that is, there can be no more than one edge between any two vertices. A polyhedron is solid if and only if it has at least three vertices.

A polyhedron's symmetry elements form other polyhedra whose intersections with the original polyhedron define its facets. The number of facets defines the polyhedron's genus. A sphere has 0 facets and therefore has genus 0. A cube has 6 facets and thus has genus 1. More generally, a polyhedron of genus g has 2g+6 faces.

The name "polyhedron" comes from **the Greek word poli**, meaning "many", and hodos, meaning "way". Thus, a polyhedron is "a many-sided figure".

- How do you describe a solid shape?
- What is meant by "solid shapes"?
- What can you say about the shapes of solids?
- What is the surface of a solid called?
- What is the face of a solid shape?
- What are flat and solid shapes?
- What is the plane surface of a solid called?
- Why are solid shapes also called 3D shapes?

Solid forms are objects that occupy space. To put it another way, faces meet at edges, while edges meet at vertices. Cone, Cuboid, Sphere, Cube, and Cylinder are some examples of solid forms.

Cones, cubes, spheres, cylinders, and cubes are examples of solid forms. A cube has six square faces and eight right angles (90 degrees) at each vertex.

It is possible to describe the shape of any surface by giving **its dimensions** and how many times it makes a complete rotation. For example, a cubical box can be described as having length, width, and height equal to each other. It makes one face toward the front, two sides to the left, three back, four corners down, and finally one side down again.

Similarly, it is possible to describe the shape of objects with more than one face or edge by giving their dimensions and how many times they make a complete rotation. Examples include a sphere, cylinder, and torus. Spheres have diameter, radius; cylinders have height, base; and tori have **inner and outer diameters**.

These are only some examples. There are many more shapes than these. You will learn more about them as you progress in **science class**.

In mathematics, algebraic equations describe the relationship between **two or more variables**. The solutions to **these equations** define the sets of values that the variables can take on.

The word "face" is used here in **its ordinary meaning** of appearance or face.

A face of a material is any actual physical surface of that material. A face of a three-dimensional object is any plane perpendicular to the axis of rotation for that object. Faces may have **different shapes** and sizes depending on how they are defined. Rectangular faces are those that extend in two opposite directions from a point called the center of mass. They include squares, rectangles, and triangles. Cylindrical faces are those that grow out from the center of mass in a single direction. They include cylinders and cones.

Faces can also be described by their orientation. If one face is horizontal while another is vertical, they are said to have **different planes**. Objects with different numbers of faces (triangles, squares, etc.) would not usually be considered solids because there is no way to define **their interior dimensions**. However, if each face is equally sized and shaped, then they are considered solids.

The term "solid" does not only refer to objects that have dimensions that can be measured in meters or feet.

Solid forms are defined by properties such as faces, vertices, and edges. Faces are individual flat surfaces. Faces intersect in straight lines known as edges and points known as vertices. Faces are flat surfaces that are surrounded by edges. A plane or 2d figure is a solid shape's face. There can be only one plane per **solid shape**.

A sphere has no clear-cut face structure - instead there are regions of different densities. However, you can divide it up into **two general parts**: the outside and the inside. The outside is made up of three layers: the surface skin, the inner core, and the outer core. The inside consists of **just the core layer**.

A cube has **six flat surfaces** called faces which meet at right angles. Each face has three edges and one corner. A corner is where two faces meet.

A tetrahedron has **four flat surfaces** called faces which meet at right angles.

An octahedron has eight flat surfaces called faces which meet at right angles.

A dodecahedron has **twelve flat surfaces** called faces which meet at right angles.

Faces and flat surfaces are both possible for solids. These are the two-dimensional parts of a three-dimensional object (TEKS K. 6C.). A cube, for example (picture a tissue box), is made up of squares, which are the two-dimensional component of this three-dimensional structure. There are eight squares that make up one cube.

As you can see by looking at our cube, it is made up of two types of shapes: cubes and squares. All cubes are square, but not all squares are cubes. The TEKS calls **these "flat" and "solid" shapes**. Flat shapes do not have any depth; they are just layers of color on top of each other. Solids have depth and are 3-D.

The best way to think about faces and flats is that every face is flat, but not every flat is a face. For example, the side of a cube is flat, but not every side is a face. Only the front and back are faces because they have **sharp edges** that are perpendicular to the surface. As for solids, only cuboids (three-dimensional objects) are solids. Cylinders (two-dimensional objects) are flat.

This lesson was inspired by **the Texas Essential Knowledge Standards** for **Earth Science** (TEKS K.6A-B). These standards were developed by teachers from around the state to help them better teach their subjects.

A face is a planar surface of a solid that is surrounded by edges. A cube has **six faces**, a dodecahedron has 12 faces, and so on.

All of these things in space have three dimensions: breadth, length, and height or depth. Solid Shapes are defined as: Three-dimensional things are solid forms. This indicates that all solid forms have three dimensions: width, height, and depth. Although most objects we encounter in **daily life** are solid shapes, some artworks and natural phenomena such as clouds, fog, smoke, and volcanoes are also considered solid shapes.