In 4-dimensional geometry, the octahedral pyramid is bounded by one octahedron on the base and 8 triangular pyramid cells which meet at the apex. Since...

meet at the vertex the way 6 edges meet at the apex of a canonical octahedral pyramid. The 6 orthogonal central planes of the 16-cell can be divided into...

16 cubic pyramids. The 24-cell tessellates 4-dimensional space as the 24-cell honeycomb. The dual to the cubic pyramid is an octahedral pyramid, seen as...

In mathematics, a centered octahedral number or Haüy octahedral number is a figurate number that counts the points of a three-dimensional integer lattice...

square pyramids, one upside-down underneath the other, by splitting it along a square cross-section. Therefore, the n {\displaystyle n} th octahedral number...

of octahedral cells: ↔ . A second half symmetry is [3,4,1+,4]: ↔ . A higher index sub-symmetry, [3,4,4*], which is index 8, exists with a pyramidal fundamental...

tetrahedral number. The sum of two consecutive square pyramidal numbers is an octahedral number. The pyramidal numbers were one of the few types of three-dimensional...

square pyramids and tetrahedra sitting on their edges. A second slice direction needs no new faces and includes alternating tetrahedral and octahedral. This...

Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has...

irregular truncated octahedral pyramid. Because its base is a regular octahedron which is a 24-cell octahedral cell, this 4-pyramid lies on the surface...

equilateral square pyramids. Its dual polyhedron is the cube, and they have the same three-dimensional symmetry groups, the octahedral symmetry O h {\displaystyle...

digonal antiprisms. It can be seen as a net of a four-dimensional octahedral pyramid, consisting of a central octahedron surrounded by eight tetrahedra...

for AX6E1 predicts a pentagonal pyramidal shape. Pairs of octahedra can be fused in a way that preserves the octahedral coordination geometry by replacing...

rectangular pyramid vertex figure. It has a Coxeter diagram . Perspective view from center of rhombicuboctahedron The omnitruncated cubic-octahedral honeycomb...

regular 5-cell.) Octahedral pyramid, ( ) ∨ {3,4}, an octahedron base, and 8 tetrahedra sides meeting at an apex. Icosahedral pyramid, ( ) ∨ {3,5}, an...

seven-vertex apex graph that forms the skeleton of a four-dimensional octahedral pyramid. If K1,2,2,2 could be shown not to have any planar covers, this would...

Conway +1/24[O×O].23). It is called the octahedral pyramidal group and is 3D octahedral symmetry, [4,3]. A cubic pyramid can have this symmetry, with Schläfli...

common type of complex is octahedral, in which six ligands form the vertices of an octahedron around the metal ion. In octahedral symmetry the d-orbitals...

dissected into 6 square pyramids and 8 tetrahedra meeting at a central point. This dissection is expressed in the tetrahedral-octahedral honeycomb where pairs...

octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells. The boundary...

tile space together with the regular tetrahedron to form the tetrahedral-octahedral honeycomb. It occurs in nature in certain crystals, in architecture as...

In chemistry, the capped octahedral molecular geometry describes the shape of compounds where seven atoms or groups of atoms or ligands are arranged around...

neighbors. For every sphere there is one gap surrounded by six spheres (octahedral) and two smaller gaps surrounded by four spheres (tetrahedral). The distances...

A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers...

isosceles-trapezoidal pyramid vertex figure. The runcicantellated square tiling honeycomb is the same as the runcitruncated order-4 octahedral honeycomb. The...

sulfur hexafluoride (SF6) is an octahedral molecule. Trigonal pyramidal: A trigonal pyramidal molecule has a pyramid-like shape with a triangular base...

tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges...

an octahedral prism is a convex uniform 4-polytope. This 4-polytope has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms. Octahedral dyadic...

a dual to the vertex-transitive gyrated tetrahedral-octahedral honeycomb. The rhombic pyramidal honeycomb or half oblate octahedrille is a uniform space-filling...

prisms, and 6 square pyramids. The octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. The cupola...