📐 10 characteristics of "Geometric Solids"

When we talk about geometric bodies , we're referring to three-dimensional figures that occupy a space in the physical and mathematical world. They're fundamental to geometry, architecture, and even everyday life (have you ever wondered why shipping boxes are rectangular prisms?).

Below, I present 10 essential characteristics of geometric shapes, explained clearly and simply.

🔹 1. They have three dimensions

Unlike flat figures, geometric bodies have three dimensions :

• Height (what it measures vertically).
• Width (its extension from one side to the other).
• Depth (what is projected towards the bottom).

These three parameters allow an object to have volume and be measured in space.

🔹 2. They are made up of faces, edges and vertices

Every geometric body is formed by:

• Faces : the flat or curved surfaces that delimit it.
• Edges : the segments where two faces meet.



• Vertices : the points where three or more edges converge.

To visualize it better, think of a cube : it has 6 faces, 12 edges and 8 vertices.

🔹 3. They are classified into polyhedrons and round bodies

Here comes an important distinction:

• Polyhedra : they have all their faces flat (like prisms or pyramids).
• Round bodies : include curved surfaces (such as cylinders, cones and spheres).

This means that not all geometric bodies have right angles or sides.

🔹 4. They occupy a volume in space

An essential characteristic is that they have volume , that is, they occupy a space. This is measured in cubic units ( cm³, m³, liters, etc. ).

For example, a shoe box has volume, while a drawing of the same box on a sheet of paper only has area.

🔹 5. They can be convex or concave

Geometric bodies can be classified as:

• • Convex : if any segment that joins two points within the figure lies completely within it.
  • Concave : if when drawing a segment between two internal points, part of the segment remains outside the body.

"Normal" polyhedra (such as cubes or prisms) are convex, but there are concave polyhedra with faces that slope inwards.

🔹 6. They have axes and planes of symmetry

Many geometric shapes exhibit symmetry . This means we can divide them into equal parts using axes or planes.

For example, a sphere has infinite axes of symmetry , while a rectangular prism has three principal planes of symmetry .

🔹 7. Its surfaces may or may not be developable

What does this mean? A geometric solid is developable if it can be represented on a plane without distortion.

• A cube or a cylinder can be "unfolded" into a flat figure.



• A sphere , on the other hand, cannot be developed without deformations (that is why world maps are never perfect).

🔹 8. Their areas and volumes can be calculated

Each geometric body has specific formulas to calculate its area and volume.

These types of calculations are essential in architecture, physics, and many other disciplines.

🔹 9. Some have additional elements

Beyond their faces, edges and vertices, some geometric bodies include other important elements :

• Height : in pyramids and cones, it is the distance from the base to the top vertex.
• Apothem : appears in regular pyramids and prisms, helping to calculate their areas.
• Generator : in cylinders and cones, it is the segment that generates the figure when rotating a straight line.

🔹 10. They are found in nature and in everyday objects

Finally, geometric bodies are not just mathematical theory: they are everywhere .

• The sphere into planets, water drops or balls.
• The cylinder in cans, logs and pipes.
• Prisms in buildings, boxes and building blocks.

Geometry is not only studied in books, but it shapes the world we live in .

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