science

Truncated great dodecahedron

Truncated great dodecahedron is a science 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 Truncated great dodecahedron rather than just read about it. In short: In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices.

Key takeaways

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

Reference excerpt

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,5/2}.

Related polyhedra It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms.

This polyhedron is the truncation of the great dodecahedron:

The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces, 12 pentagons from the truncated vertices and 12 overlapping as (truncated pentagrams).

Small stellapentakis dodecahedron

The small stellapentakis dodecahedron (or small astropentakis dodecahedron) is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.

Illustrations

Worked examples

Example 1 — a first encounter with Truncated great dodecahedron

Start with the simplest possible case. Write down what Truncated great dodecahedron claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Truncated great dodecahedron 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 Truncated great dodecahedron 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 Truncated great dodecahedron

In research: Truncated great dodecahedron appears in science 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 Truncated great dodecahedron 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: Truncated great dodecahedron is common in secondary-school and first-year university syllabi. It links to neighbouring topics Nonconvex polyhedra, Polyhedron stubs, Uniform polyhedra, so understanding it makes those chapters shorter.
In everyday life: Look for Truncated great dodecahedron 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 Truncated great dodecahedron in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Truncated great dodecahedron 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 Truncated great dodecahedron out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Truncated great dodecahedron in simple terms?

In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices.

Why does Truncated great dodecahedron matter?

Because it connects several science 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 Truncated great dodecahedron?

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 Truncated great dodecahedron.