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Q&A Dividing a cuboid in four

1 answer  ·  posted 1y ago by Yair Rand‭  ·  last activity 1y ago by Peter Taylor‭

Question geometry
#2: Post edited by user avatar Yair Rand‭ · 2022-12-16T03:03:21Z (over 1 year 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.
  • ![Diagram](https://math.codidact.com/uploads/vp4c56pidtgywkzvum2l3pwtxcz6)
  • 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.
  • ![Diagram](https://math.codidact.com/uploads/vp4c56pidtgywkzvum2l3pwtxcz6)
  • How might one determine coordinates for I, J, K, L, M, N and O, that satisfy these constraints?
#1: Initial revision by user avatar Yair Rand‭ · 2022-12-16T03:02:31Z (over 1 year 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.
![Diagram](https://math.codidact.com/uploads/vp4c56pidtgywkzvum2l3pwtxcz6)

How might one determine coordinates for I, J, K, L, M, N and O, that satisfy these constraints?