Polyhedron

Polyhedron [pol-ee-hee-druhn]
Noun
A polyhedron is a 3D solid figure which is composed of a collection of polygons as their faces.

Cube	Triangular Prism	Dodecahedron
Its faces are all squares	Its faces are triangles and rectangles	Its faces are pentagons

*All of the above figure are polyhedrons 

Lateral Face

Lateral Face [lat-er-uhl feys]
Noun

Lateral face is the face which are not the base, the face which compliment the base. They are formed by lateral edges.  

he figure above has a hexagon as base, hence the name hexagonal prism. There are 6 lateral edges which help form and connect the 6 lateral faces. 

Lateral Edge

Lateral Edge [lat-er-uhl ej]

Noun 

A lateral edge are the edges and points which form the lateral faces of a 3D figure.   

The figure above has a pentagon as base, hence the name pentagonal prism. There are 5 lateral edges which help form and connect the 5 lateral faces. 

Base

Base [beys]
Noun
A base is one side (in solid geometry a base can also be one or two faces)  of a polygon most commonly used as a reference for other measurements such as: area, surface area, perimeter, volume etc.

 

Triangles                            Quadrilaterals with a Pair of  Parallel Sides              Faces of a Solid 

A base are usually used in triangles, quadrilaterals with a pair of  parallel sides and faces of a solid figure. Definitely a key component to geometry allowing as to find wanted measurements of both two dimensional and three dimensional figures.  

Face

Face [feys]
Noun
In any 3D shape that is composed of flat surfaces, each of these surfaces are called a face. The line where two faces meet are considered an edge.  

For example, the triangular prism above has 5 faces, 2 of them being a triangle and the other 3 being rectangles. Also in this prism there are 9 edges.    

Edge

Edge [ej]
Noun
In a 3D shape that is composed and produced of faces, an edge is a line segment where two surfaces meet. Where 3 or more edges meet, a vertex is created.  

  

The rectangular prism above there are 6 faces, therefore since an edge is where two surfaces meet, there are 12 edges in the solid figure.  

Vertex

   

Vertex [vur-teks]
Noun
Plural: vertices [vur-tuh-seez]

A vertex is a common endpoint of two or more rays/line segments. 

Usually a vertex is a point/location where 2 lines meet.They are extremely important, a necessity in geometry especially when talking about shapes and figures. They can be used in 2D (a square has four vertices) and even with solid geometry, where since it is in a 3D plane, vertices are the point where 3 or more edges meet. Also in solid geometry, a vertex can also be called a corner.