-
Sydler and Børge
Jessen studied orthoschemes extensively in
connection with Hilbert's
third problem.
Orthoschemes, also
called path-simplices in the...
- edge. The 4-cube can be
dissected into 24 such 4-
orthoschemes eight different ways, with six 4-
orthoschemes surrounding each of four
orthogonal √4 tesseract...
- 3-
orthoschemes,
three left-handed and
three right-handed (one of each at each cube face), and
cubes can fill space, so the
characteristic 3-
orthoscheme...
-
these characteristic orthoschemes surrounding the octahedron's center.
Three left-handed
orthoschemes and
three right-handed
orthoschemes meet in each of the...
-
necessary to
contain the
original Hadwiger's
conjecture on
dissection into
orthoschemes Hadwiger–Nelson
problem on the
chromatic number of unit
distance graphs...
- Hugo
Hadwiger that
every simplex can be
dissected into
orthoschemes,
using a
number of
orthoschemes bounded by a
function of the
dimension of the simplex...
-
bounded by
regular tetrahedron cells,
their characteristic 5-cells (4-
orthoschemes) are
different tetrahedral pyramids, all
based on the same characteristic...
-
Dissection of a cube into
orthoschemes. In the cube, each new edge
introduced in this
dissection is
surrounded by
dihedral angles that sum to π {\displaystyle...
-
Euclidean simplex in
terms of its
dihedral angles, and the Schläfli
orthoscheme, a
special simplex with a path of right-angled dihedrals, come from Schläfli's...
-
tetrahedron that is also a Schläfli
orthoscheme.
There are
infinitely many face cuboids, and
infinitely many
Heronian orthoschemes. The
smallest solutions for...
