So a " 2 "-parallelotope is a parallelogon which can also include certain hexagons, and a " 3 "-parallelotope is a parallelohedron, including 5 types of polyhedra.
12.
So a " 2 "-parallelotope is a parallelogon which can also include certain hexagons, and a " 3 "-parallelotope is a parallelohedron, including 5 types of polyhedra.
13.
If a-form is thought of as measuring the flux through an infinitesimal-parallelotope, then its exterior derivative can be thought of as measuring the net flux through the boundary of a-parallelotope.
14.
If a-form is thought of as measuring the flux through an infinitesimal-parallelotope, then its exterior derivative can be thought of as measuring the net flux through the boundary of a-parallelotope.
15.
In general, there does not exist a natural concept of a " volume " for a parallelotope generated by vectors in a " n "-dimensional vector space " V ".
16.
From geometric algebra, we interpret the pseudoscalar e _ 1 \ wedge e _ 2 \ wedge \ cdots \ wedge e _ n to be the signed volume of the " n "-parallelotope subtended by these basis vectors.
17.
Similarly, the volume of any " n "-simplex that shares " n " converging edges of a parallelotope has a volume equal to one 1 / " n ! " of the volume of that parallelotope.
18.
Similarly, the volume of any " n "-simplex that shares " n " converging edges of a parallelotope has a volume equal to one 1 / " n ! " of the volume of that parallelotope.
19.
The edges radiating from one vertex of a " k "-parallelotope form a " k "-frame ( v _ 1, \ ldots, v _ n ) of the vector space, and the parallelotope can be recovered from these vectors, by taking linear combinations of the vectors, with weights between 0 and 1.
20.
The edges radiating from one vertex of a " k "-parallelotope form a " k "-frame ( v _ 1, \ ldots, v _ n ) of the vector space, and the parallelotope can be recovered from these vectors, by taking linear combinations of the vectors, with weights between 0 and 1.
