Three dimension shapes

The shapes which can be measured in 3 directions are called three-dimensional shapes. These shapes are also called solid shapes. Length, width, and height (or depth or thickness) are the three measurements of the three-dimensional shapes. They are different from 2D shapes because they have thickness. A number of examples can be found in everyday life. Some of them are:

Three Dimensional Shapes

The Rubik’s Cube is an example of a cube, the drum is a cylinder, the birthday cap is a cone and the orange is a sphere.

Faces, Edges and Vertices

Three-dimensional shapes have many attributes such as faces, edges and vertices. The flat surfaces of the 3D shapes are called the faces. The line segment where two faces meet is called an edge. A vertex is a point where 3 edges meet.

Let us consider a few shapes to learn about them.

Cube

• All edges are equal
• 8 vertices
• 12 edges
• 6 faces.

Cuboid

• 8 vertices
• 12 edges
• 6 faces

Prism

• 6 vertices
• 9 edges
• 5 faces – 2 triangles and 3 rectangles

Square Pyramid

• 5 vertices
• 8 edges
• 5 faces

Cylinder

• No vertex
• 2 edges
• 2 flat faces – circles
• 1 curved face

Cone

• 1 vertex
• 1 edge
• 1 flat face – circle
• 1 curved face

Sphere

• No vertex
• No edges
• 1 curved face
• 
  
• REFERENCE FROM   https://byjus.com/maths/three-dimensional-shapes/

Polygon

Definition of a Polygon

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides. So, any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral.

Polygons

All of these shapes are polygons. Notice how all the shapes are drawn with only straight lines? This is what makes a polygon. If the shape had curves or didn't fully connect, then it can't be called a polygon. The orange shape is still a polygon even if it looks like it has an arrow. All the sides are straight, and they all connect. The orange shape has 11 sides.

I've mentioned a few polygons and have shown you a few common shapes. Here is a list of those in addition to several more:

Shape	# of Sides
Triangle	3
Square	4
Rectangle	4
Quadrilateral	4
Pentagon	5
Hexagon	6
Heptagon	7
Octagon	8
Nonagon	9
Decagon	10
n-gon	n sides

The last entry includes the general term for a polygon with n number of sides. Polygons aren't limited to the common ones we know but can get pretty complex and have as many sides as are needed. They can have 4 sides, 44 sides, or even 444 sides. The names would be 4-gon, or quadrilateral, 44-gon, and 444-gon, respectively. An 11-sided shape can be called an 11-gon.

Regular Polygons

A special class of polygon exists; it happens for polygons whose sides are all the same length and whose angles are all the same. When this happens, the polygons are called regular polygons. A stop sign is an example of a regular polygon with eight sides. All the sides are the same and no matter how you lay it down, it will look the same. You wouldn't be able to tell which way was up because all the sides are the same and all the angles are the same.

When a triangle has all the sides and angles the same, we know it as an equilateral triangle, or a regular triangle. A quadrilateral with all sides and angles the same is known as a square, or regular quadrilateral. A pentagon with all sides and angles the same is called a regular pentagon. An n-gon with sides and angles the same is called a regular n-gon.

Regular polygons

Here is a regular triangle, a regular quadrilateral, and a regular pentagon. Do you see how all the sides are the same and no matter how you flip it, it will look the same?

Angles of Regular Polygons

Regular polygons also have two different angles related to them. The first is called the exterior angle, and it is the measurement between the shape and each line segment when you stretch it out past the shape.

REFERENCE FROM  https://study.com/academy/lesson/what-is-a-polygon-definition-shapes-angles.html

Geometrical shapes

A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object.^[1] That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape.

Objects that have the same shape as each other are said to be similar. If they also have the same scale as each other, they are said to be congruent.

Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called polygons and include triangles, squares, and pentagons. Other shapes may be bounded by curves such as the circle or the ellipse.

Many three-dimensional geometric shapes can be defined by a set of vertices, lines connecting the vertices, and two-dimensional facesenclosed by those lines, as well as the resulting interior points. Such shapes are called polyhedrons and include cubes as well as pyramids such as tetrahedrons. Other three-dimensional shapes may be bounded by curved surfaces, such as the ellipsoid and the sphere.

A shape is said to be convex if all of the points on a line segment between any two of its points are also part of the shape.

REFERENCE FROM WIKIPEDIA