Creating models in Application Such as Blender requires you to be able to control the geometry and topology of your model so that you can reshape the model however you see fit. This involves knowing what the three forms of geometry are and how they behave with each other.
To join a vertex to an existing edge, select one of the vertices used to create that edge, then select the extra vertex, and use the J key to join the two vertices together to form a new edge. You can also use the F key to connect multiple vertices together and construct a face.
Knowing how your geometry works is important before you can control it and build up the topology that you want to use for your model. The first step is in knowing how your geometry is constructed.
Understanding The Three Types Of Geometry
When working with mesh objects we are using polygonal geometry to create the structure. Three types of geometry are used to build the model, and they are all dependent on each other to various degrees.
 A vertex is a single geometric coordinate in 3D space, has no form of its own, and is the building block to all geometric models in Blender.
 An edge is a single straight line that connects two vertices together. It is used to create the outline of the object by connecting edges together and forming the object’s shape.
 A face is a generally flat surface that can be created when you have three or more edges in a closed loop. This surface is what gives all objects their actual appearance in the 3D viewport and is what we use to apply materials to.
This structure is hierarchical. meaning that some forms of geometry are dependent on others. An edge is always constructed from two vertices, never more or less, and cannot exist without those vertices.
A face can only exist from a closed loop of at least three edges where the vertices connect together, and so requires the use of both edges and vertices to exist.
Knowing this, we can tell that adding a vertex in the middle of an edge divides that edge into two because no edge has more than two vertices. Likewise deleting a vertex will delete any other forms of geometry that are dependent on it. In the example below we have a subdivided cube.
One vertex is selected here, and by pressing the delete key and select vertex we not only delete the selection but all the faces and edges that were dependent on that vertex being there.
Joining Vertices Together To Create Edges And Faces
Let’s use the subdivided cube to demonstrate how joining works in edit mode. We have a hole in our cube and we want to fill it with new geometry. The idea here is to create a diamond shape and then delete the diamond to create a shaped window.
We have a total of 8 vertices to work with here, but we are not going to use the ones that create the corners of the hole. Select two vertices that are not directly connected together, such as the top vertex and the left side vertex.
Two hotkeys will allow us to connect the selected vertices together but in different ways. The F key is designated as the fill key, meaning it will connect the two at the shortest point in between, as seen in the image below.
This is the shape that we are looking for to create the diamond hole, as it creates a short diagonal line in between our selected vertices even though there is nothing else here.
By contrast, the J key is used to join your selection based on existing vertex paths, meaning it looks for a route using the geometry that already exists. This has a very different effect on the models’ topology below.
The effect on your geometry here is almost inverted between the two, so the choice that you make here depends on what you are trying to create. For use we want to form that shape in the gap, so we will use the first option to create that shape.
By connecting each of the side edges together by selecting them pair by pair and then using the F key, we are able to fill the spaces in between and attain our shape.
Much as vertices can be joined together to form new edges, those edges can be used to form new faces. To create a new face, select at least two of the edges that are required to make that face and then use the F key to fill the space. Even if you have not selected all the edges Blender is smart enough to know how to connect them.
This will leave us with the diamond shaped hole in the middle, which is exactly what we were going for.
How Connecting Vertices Affects Your Model
Whether you are creating new edges, vertices, or faces, even when you are deleting them, you need to be aware that the changes to your model can be both positive and negative.
For example, in quadbased models where foursided faces are used, loops are created that you can both select and manipulate.
Any face that is not a quad creates a pole, where Blender no longer knows where to send the loop and so ends the selection before reaching the pole face.
For example, the faces that we created for our shape are triangles, meaning they act as poles for our loop. By using the alt key, we can select a loop of vertices, edges, or faces. Below we select a loop of faces and you can see where the loop ends.
Changing the topology will impact the certain materials applied to the model, and how rigging affects the animated properties of the object.
Another factor to consider is vertex density. When sculpting for example this is almost completely ignored, but for standard modeling, you need to ensure that all areas of your model use the minimum amount of geometry required to fulfill its purpose.
Like any realworld object, the more parts there are to a model the more points of potential failure there are. Make sure to only add geometry where the geometry is needed, as every vertex changes the way a model behaves.
I Have Messed Up My Geometry, So How Do I Fix It?
When you begin to create your own edges without using tools like loop cuts, you begin to change the topology of the model and sometimes this can result in poorly constructed shapes or geometry that ends up being redundant.
There are two basic rules to follow when you are using tools like the fill and join tools to construct new geometry.
 Make sure that you avoid creating nonmanifold geometry where possible. Nonmanifold means any form of geometry that would not be able to exist as a shape in the real world. For example when you extrude a single edge out from a cube and have no faces connected to either side.
 Your vertices should be far enough apart so that they do not risk overlapping, which can cause artifacts in shading, texturing, and animation behavior.
The example cube above is technically a nonmanifold object, as it has no thickness yet we can see both inside and outside. A quick solution is to add a solidify modifier to the cube.
If you have any vertices that are redundant to the shape of the model, then you can dissolve that geometry rather than delete it. Select the geometry and press the delete key to open the menu, then select one of the dissolve options.
With dissolving, the geometry that was dependent on the vertex is reconstructed, with the edges merging together to reduce the number of faces surrounding the area.
If you have overlapping geometry, you can clean this up by using the merge tool, which is accessed by using the M key. The easiest option is to merge by distance, which we quickly tidy up areas where the geometry is overlapping the same space.
Thanks For Reading The Article
We appreciate you taking the time to read through the article and we hope you found the information that you were looking for. Below we have compiled a list of additional topics that you may be interested in reading.
 Clean Up Your Model After Using A Boolean
 Using Smooth Shading And The Auto Smooth Tool
 Keeping Sharp Edges When Using The Subdivision Surface Modifier
 Retopologize Your Model The Fast Way
 Unsubdivided A Model To Reduce Geometry

Custom Normals: Blender Hard Surface Tip
Enhancing hard surface models with custom normals for realism.

Align Perfectly with Blender’s Snap Tools
Aligning objects perfectly with Blender’s advanced Snap tools.