How to create any dimensional object in geometry (shortened version)

 1.  If you   want an object to exist at a particular dimensional realm, then you need the node particle or  point that has the adequate amount of elements for that number of dimension. 

1.b as with spherical coordinates though we have 3 elements for both Cartesian and spherical to have a point in 3 Dimensional space , we just need to be able to infer or decide what the spatial coordinates are, and assume all spatial dimensional are the same as cartesian. That is to say that Cartesian coordinate system can describe every point which is described by another coordinate system. 

Then when you have the point and it's coordinate system.

2. Create the one simplex, as a collection of 2 points.

You can see how a vector with direction because it is a line between start and end. 

3. Create the two simplex as a collection of 2 one simplices.  

You can see in matrix algebra how a pair of line vectors forms a the triangle which represents it's coplanar infinite  plane. 

4. Create the three simplex as a collection of 2 two simplices. 

You can see how a tetrahedron is pair of equilateral triangles. One standing up in the 3D. But as a different pair  you can see that there is the base triangle, and then the vertical triangle spawns  a stack of parallel, intregrand triangles , as they shrink in size. Proportionally relating the length and radius at a rate so that the side of the stack is also an equilateral triangle. 

5. Create the four simplex to incorporate time. 

When you discover something new and have to update the point, and the spatial rendering mechanism ,

THEN MAKE SURE TO REITERATE THROUGH THE DIMENSIONAL STACK AGAIN.