The axis is a line around which spaces and forms are organized. It is not a visible line, the axis can be strongly evident, powerful and dominating as it is this image, where the large fireplace plane forms the central axis. There are also evidence of secondary axis in this image in the perspective view of the window and the wood paneled wall.
There are two basic types of symmetry, bilateral and radial. Bilateral symmetry is balance that is achieved through the arrangement of similar elements on either side of a central axis line, so that the two half's are almost mirror images of each other. While radial symmetry is balance that achieved with the arrangement of radiating elements.
This image shows an example of bilateral symmetry. It can be divided down the center with each element reflected or with an equivalent element on the other.
Hierarchy is simply the principle that helps to show significance or importance in an form or space. It's importance is denoted by the either by its size, shape, or placement in relationship to other objects.
The simplest example that popped into my head is the size relationship between a headboard and a foot board. This image show how traditionally the headboard is larger and more prominent in the design of the bed as it denotes where the head is placed.
Rhythm and Repetition
Rhythm is design is characterized by a series of repeated elements that creates unity. While repetition is duplication of an element to form a pattern. These principles are often used together as they help to emphasis a trait in the design.
In this room elements of repetition and rhythm are evident, in the use of identical chairs and also in the herringbone or zig-zag pattern of the rug.
Transformation
Transformation is the principle in which forms can be altered by a series of manipulations. This room has many different configurations as a result of the transformation of this gridded wall changing into a three piece bathroom.
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