so a tensor which would be a group of all vectors defined by SO(4), would be a tensor of all the possible 4d views? so bi-glomohedric prism, a terix in 6d, can be considered a tensor? now i am confused.
A tensor is a means of taking two vectors and making an output vector. It is not a set of vectors, just a vector with two or more subscripts. For example, the cross-product in three-dimensions is a tensor.
One often finds tensors where one has a multi-directional vector (ie the size depends on the direction). Magnetism makes use of tensors.
The bi-glomohedric prism is simply what the physicists would call a representation in a phase-space: each point of the prism represents a valid phase (here a great-arrow in 4d).
What you do with a phase-space is to plot out the kind of motion that might arise when something changes. For example, the complete phase space for rotations in 4d is a bi-glomohedric pyramid. The natural tendancy for rotations is to move to one of the bases of the pyramid. This would be represented by a path in phase-space.
It's best to think of matrices as arithmetic processes [ie something you do with numbers], and tensors as some kind of physical process [like a whirlywind]. One might describe a tensor by a matrix.
The bi-glomohedric prism and pyramid, are phase-spaces, which represent each possible state of great-arrows and rotations in general, as points on a surface. When something changes rotation-mode, then the point representing its motion moves on the phase-space.
Wendy