chemistry

Polyhedral symbol

Polyhedral symbol is a chemistry topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Polyhedral symbol rather than just read about it. In short: The polyhedral symbol is sometimes used in coordination chemistry and crystallography to indicate the approximate coordination geometry around the central atom. One or more italicised letters indicate the geometry, e.g.

Key takeaways

Polyhedral symbol belongs to chemistry; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Polyhedral symbol to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Polyhedral symbol from memory before moving on to harder problems.

Reference excerpt

The polyhedral symbol is sometimes used in coordination chemistry and crystallography to indicate the approximate coordination geometry around the central atom. One or more italicised letters indicate the geometry, e.g. TP-3 which is followed by a number that gives the coordination number of the central atom. The polyhedral symbol can be used in naming of compounds, in which case it is followed by the configuration index.

Polyhedral symbols

Configuration index Source: The first step in determining the configuration index is to assign a priority number to each coordinating ligand according to the Cahn-Ingold-Prelog priority rules, (CIP rules). The preferred ligand takes the lowest priority number. For example, of the ligands acetonitrile, chloride ion, and pyridine the priority number assigned are chloride, 1; acetonitrile, 2; pyridene, 3. Each coordination type has a different procedure for specifying the configuration index and these are outlined in below.

T-shaped (TS-3) The configuration index is a single digit which is defined as the priority number of the ligand on the stem of the "T".

Seesaw (SS- 4) The configuration index has two digits which are the priority numbers of the ligands separated by the largest angle. The lowest priority number of the pair is quoted first.

Square planar (SP-4) The configuration index is a single digit which is the priority number of the ligand trans to the highest priority ligand. (If there are two possibilities the principle of trans difference is applied). As an example, (acetonitrile)dichlorido(pyridine)platinum(II) complex where the Cl ligands may be trans or cis to one another. The ligand priority numbers are, applying the CIP rules:

two chlorides of priority number 1 acetonitrile priority 2 pyridine priority 3 In the trans case the configuration index is 1 giving the name(SP-4-1)-(acetonitrile)dichlorido(pyridine)platinum(II). In the cis case both of the organic ligands are trans to a chloride so to choose the trans difference is considered and the greater is between 1 and three therefore the name is (SP-4-3)-(acetonitrile)dichlorido(pyridine)platinum(II).

Octahedral (OC-6) The configuration index has two digits. The first digit is the priority number of the ligand trans to the highest priority ligand. This pair is then used to define the reference axis of the octahedron. The second digit is the priority number of the ligand trans to the highest priority ligand in the plane perpendicular to the reference axis.

Square pyramidal (SPY-4) The configuration index is a single digit which is the priority number of the ligand trans to the ligand of lowest priority in the plane perpendicular to the 4 fold axis. (If there is more than one choice then the highest numerical value second digit is taken.) NB this procedure gives the same result as SP-4, however in this case the polyhedral symbol specifies that the complex is non-planar.

Square pyramidal (SPY-5) There are two digits. The first digit is the priority number of the ligand on the fourfold (C4) axis of the idealised pyramid the second digit is the priority number of the ligand trans to ligand of lowest priority in the plane perpendicular to the 4 fold axis. (If there is more than one choice then the highest numerical value second digit is taken.)

Trigonal bipyramidal (TBPY-5) The configuration index consists of two digits which are the priority numbers of the ligands on the threefold rotation axis. The lowest numerical value is cited first.

Other bipyramidal structures (PBPY-7, HBPY-8 and HBPY-9) The configuration index consists of two segments separated by a hyphen. The first segment consists of two digits which are the priority numbers of the ligands on the five, six or sevenfold rotation axis. The lowest numerical value is cited first. The second segment consists of 5, 6 or 7 digits respectively. The lowest priority number is the first digit followed by the digits of the other atoms in the plane. The clockwise and anticlockwise sequences are compared and the one that yields the lowest numerical sequence is chosen.

References

Worked examples

Example 1 — a first encounter with Polyhedral symbol

Start with the simplest possible case. Write down what Polyhedral symbol claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Polyhedral symbol before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Polyhedral symbol ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Polyhedral symbol

In research: Polyhedral symbol appears in chemistry research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Polyhedral symbol in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Polyhedral symbol is common in secondary-school and first-year university syllabi. It links to neighbouring topics Coordination chemistry, Molecular geometry, so understanding it makes those chapters shorter.
In everyday life: Look for Polyhedral symbol outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Polyhedral symbol in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Polyhedral symbol means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Polyhedral symbol out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Polyhedral symbol in simple terms?

Why does Polyhedral symbol matter?

Because it connects several chemistry ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Polyhedral symbol?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Polyhedral symbol.