Done by: Mohammed E.
Al-Dhafeeri
Introduction
I have prepared this document that will show the difference/definitions of each
Dimensional model (3D, 4D and 5D). To be honest I got lost while searching in Google, I
got many topics about 3D, 4D and 5D, and it turns out that those dimensions are exist in
many fields; emotions “research by Jim Self”, also those dimensions present in
services/business which I will describe below, and finally those dimensions are in
Graphics that will be explained below. I will be talking about the Business side when
using those dimensions and the Graphics side.
Figure shows 1D, 2D, 3D, 4D and 5D
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Done by: Mohammed E. Al-Dhafeeri
Three Dimensional Models
To simplify this section I would like to present an image that will briefly explain
what are the One Dimension (1D), Two Dimensions (2D) and Three Dimensions (3D).
1D 3D
2D
In physics and mathematics, the dimension of a space or object is informally
defined as the minimum number of coordinates needed to specify each point within it.
Thus a line has a dimension of one because only one coordinate is needed to specify a
point on it. A surface such as a plane or the surface of a cylinder or sphere has a
dimension of two because two coordinates are needed to specify a point on it (for
example, to locate a point on the surface of a sphere you need both its latitude and its
longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three
co-ordinates are needed to locate a point within these spaces.
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Done by: Mohammed E. Al-Dhafeeri
Four Dimensional Models
Algebraically it is generated by applying the rules of vectors and coordinate
geometry to a space with four dimensions. In particular a vector with four elements (a 4-
tuple) can be used to represent a position in four-dimensional space. The space is a
Euclidean space, so has a metric and norm, and so all directions are treated as the same:
the additional dimension is indistinguishable from the other three.
In modern physics, space and time are unified in a four-dimensional Minkowski
continuum called spacetime, whose metric treats the time dimension differently from the
three spatial dimensions. Spacetime is thus not a Euclidean space.
This image demonstrates the Fourth Dimension (4D): “It is an animated image; I attached to
the document this image, kindly open it to see it working”
The 4D is also called “Spacetime”. In physics, spacetime (or space–time, space
time) is any mathematical model that combines space and time into a single continuum.
Spacetime is usually interpreted with space as being three-dimensional and time playing
the role of a fourth dimension that is of a different sort from the spatial dimensions.
According to certain Euclidean space perceptions, the universe has three dimensions of
space and one dimension of time. By combining space and time into a single manifold,
physicists have significantly simplified a large number of physical theories, as well as
described in a more uniform way the workings of the universe at both the supergalactic
and subatomic levels.
The Fourth Dimension in Business means: A 4D model looks just like a 3D model, but
it contains even more information about installation rates, productivity rates, crew sizes,
and costs.
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Done by: Mohammed E. Al-Dhafeeri
Fifth Dimensional Models
In physics and mathematics, a sequence of N numbers can be understood to
represent a location in an N-dimensional space.
Abstract five-dimensional space occurs frequently in mathematics, and is a
legitimate construct. Whether or not the real universe in which we live is somehow five-
dimensional is a topic that is debated and explored in several branches of physics,
including astrophysics and particle physics.
In five or more dimensions, only three regular polytopes exist. In five dimensions,
they are:
1- The 5-simplex of the simplex family, with 6 vertices, 15 edges, 20 faces (each an
equilateral triangle), 15 cells (each a regular tetrahedron), and 6 hypercells (each a
5-cell).
2- The 5-cube of the hypercube family, with 32 vertices, 80 edges, 80 faces (each a
square), 40 cells (each a cube), and 10 hypercells (each a tesseract).
3- The 5-orthoplex of the cross polytope family, with 10 vertices, 40 edges, 80 faces
(each a triangle), 80 cells (each a tetrahedron), and 32 hypercells (each a 5-cell).
A fourth polytope can be constructed as an alternation of the 5-cube, and is called a 5-
demicube, with half the vertices (16), bounded by alternating 5-cell and 16-cell
hypercells.
5D Cube
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Done by: Mohammed E. Al-Dhafeeri
The Fifth Dimension in Business: a 5D model looks just like a 3D model, but it
includes component pricing and budgeting reports for the job.
Conclusion
What we saw above were really brief to each N-Dimension, I hope I did picked up
the best information that will help in developing our knowledge about these Dimensions
in our work. I will summarize the usage of each N-Dimension as follows:
• 3D can be used only for clients; we can use this module to demonstrate our work
briefly to the customer. By showing the client the 3D module he will know/or he
will get general idea of how the project will look like. Maybe we can use it in the
initialization stage/phase!
• 4D can be used also to demonstrate things to the client but in more details and
more clarifications. So, using 4D will give the client more impact of how things
are going to be when the project is done. It is actually a 3D module with more
information and one more dimension.
• 5D this we use it when we need to give all details, more details regarding the
project, more complex and it gives a very clear vision of the whole project with
detailed information about it. It demonstrates the whole project. This might be
hard to show to the client since he might misunderstand it or have lack vision. So,
it is better to use it for the Design departments and Architecture department, as a
result, they will know exactly how the whole project will look like and things will
go smoothly while working on the project since everything is clear to them.
• Finally, put this all together and you get the iterative effect of 3D-4D-5D. As the
model grows in complexity, it becomes the data-rich font of project knowledge.
Each stakeholder can approach the model with different questions and what-if
scenarios and receive near-instant analysis of the situation.
References
• http://www.vicosoftware.com/3D-4D-5D-BIM-Modeling-
Services/tabid/79439/Default.aspx
• http://en.wikipedia.org/wiki/Five-dimensional_space
• http://www.gravitation3d.com/magiccube5d/
• http://phillips.blogs.com/goc/2008/04/dimensions.html
• http://en.wikipedia.org/wiki/Convex_regular_4-polytope
• http://en.wikipedia.org/wiki/Fourth_dimension
• http://en.wikipedia.org/wiki/Spacetime
• http://en.wikipedia.org/wiki/Dimension
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