In a three dimensional sense, we may think of a x, y, and z coordinate plane having both its positive and negative coordinate systems. The molecule below has no lone pairs of electrons surrounding it, thus allowing it to have a distinct shape. There are six bonding pairs in this molecule and no lone electron pairs. What makes this molecule different from other species is the fact that it is surrounded by six, either the same or different, atoms. We will begin by describing the design of an octahedral and then continue on to the next two molecules.Īn octahedral is best described as a central atom symmetrically arranged by six other atoms. This allows one to recognize and see the difference in the molecular design for each individual molecule. A simple comprehension of geometry is required to be able to imagine molecules in 3D, as well as having basic background knowledge of the concept of bonding pairs and lone pairs. To be able to understand and distinguish the difference between the three types of octahedral species and how they differ from one molecule to the next, it is essential to try to visualize shapes geometrically and in 3D. This allows us to distinguish and classifiy the octahedrals based on the following shapes: octahedral, square pyramidal, and square planar. In regards to identifying each species, we will be looking at three separate unique shapes with different numbers of bond pairs and lone pairs. All atoms are 90 degrees apart from one another, and 180 degrees apart from the atom, directly across and opposite from it. The prefix octa, which means eight, comes from the fact that the molecule has eight symmetrical faces. Our ready to fold kits are still available at: In inorganic chemistry, an octahedron is classified by its molecular geometry in which its distict shape is described as having six atoms, groups of atoms or electron pairs symmetrically arranged around one central atom, defining the vertices of an octahedron. With two more Hexahedrons, you can reassemble to create the linked loop shown. I won't tell anyone, but as always, be precise! Note: If you do not have access to A5 sheets, you can always cut your A4 paper in half. The pattern for it's net, shown here, would serve equally well as a hinging diagram, creating the same "space-filled" model. One can easily see how 12 of these individual units, The A5 Rhombic Pyramid, could be linked to form our Rhombic Dodecahedron. The photos now show 4 complete Rhombic Hexahedrons, linked, then folded, to form the dodecahedron. Make three folds to divide the sheet in four equal parts along its long length.įold diagonals from center of long lengths to corners. To maintain the proper scale for our model, the A5 fold pattern is as follows: And finally we will see how four of these would fill the voids found in our Rhombic Dodecahedron. I will now show how we can model a single Rhombic Pyramid from one sheet of A5 paper to complete the hexahedron. As the chart tell us, the complete hexahedron requires 3 such pyramids, thus the voids in our model. This creates a figure forming two thirds of the Rhombic Hexahedron seen in the chart. The form we modeled today from our single sheet of A4 paper consists of a cluster of two of these Rhombic Pyramids, sharing sides, not bases. Turned 90 degrees, with the rhombus in the horizontal plane, it reads as The Rhombic Dipyramid. This figure is in fact identical to our own square based Dipyramid, and is shown as such in the chart. We can see from Inchbald's flow-chart how a pair of these pyramids, sharing their rhombic bases, will form a dipyramid, what he calls The Oblate Octahedron. This is the figure that we found two of, hinged together, that we called attention to in Step 2 of this Instructable. The third, the pyramid, has the rhombus as its base, and 4 similar isosceles triangles, each one equal to one half of the rhombus, completing the figure. It's proportions are defined in the diagram I've borrowed from Mathworld.* The surfaces of the first two of these, dodecahedron and hexahedron, are made up exclusively of these rhombic faces. The rhombi associated with the first three named above, are the ones found in our fold pattern. The Rhombic Hexahedron (a Parallelepiped)Īnd, of course, what he calls The Oblate Octahedron, which is the same as our basic figure, The DIN A Dipyramid. I present the chart not just for its graphic clarity, but also so that we may borrow from its nomenclature. In this chart we recognize some of the geometries imbedded in DIN A paper that drive my Instructables. Here, I reproduce a chart from his article "The Archimedean Honeycomb Duals", which can be found on his website.
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