Post History
Question
geometry
#2: Post edited
by
Yair Rand
·
2022-12-16T03:03:21Z (about 2 years ago)
(line break)
- Suppose we have an irregular cuboid (that is, a hexahedron with six irregular quadrilateral faces) ABCDEFGH that we wish to divide into four smaller cuboids, such that three of them each fully share a face with one of the outer cuboid's three faces adjacent to point H (so, JKCDNOGH, IBKDMFOH, and LMNOEFGH in the diagram), and the fourth cuboid shares a vertex with opposite point A (thus AIJKLMNO in the diagram), and such that each of the four cuboids has equal volume.
- 
- How might one determine coordinates for I, J, K, L, M, N and O, that satisfy these constraints?
- Suppose we have an irregular cuboid (that is, a hexahedron with six irregular quadrilateral faces) ABCDEFGH that we wish to divide into four smaller cuboids, such that three of them each fully share a face with one of the outer cuboid's three faces adjacent to point H (so, JKCDNOGH, IBKDMFOH, and LMNOEFGH in the diagram), and the fourth cuboid shares a vertex with opposite point A (thus AIJKLMNO in the diagram), and such that each of the four cuboids has equal volume.
- 
- How might one determine coordinates for I, J, K, L, M, N and O, that satisfy these constraints?
#1: Initial revision
by
Yair Rand
·
2022-12-16T03:02:31Z (about 2 years ago)
Dividing a cuboid in four
Suppose we have an irregular cuboid (that is, a hexahedron with six irregular quadrilateral faces) ABCDEFGH that we wish to divide into four smaller cuboids, such that three of them each fully share a face with one of the outer cuboid's three faces adjacent to point H (so, JKCDNOGH, IBKDMFOH, and LMNOEFGH in the diagram), and the fourth cuboid shares a vertex with opposite point A (thus AIJKLMNO in the diagram), and such that each of the four cuboids has equal volume.  How might one determine coordinates for I, J, K, L, M, N and O, that satisfy these constraints?