LEARN · EXPLAIN · REVISE

Verify Euler’s relation for an 12-gonal prism by giving V,E,F.

Read the idea, work independently, then explain what changed.

TOPIC 01

Introduction to solid geometry: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Identify the defining faces, cross-sections and generating elements of the solid.

Hint 2

Count two bases and n lateral faces.

Worked solution

Identify the defining faces, cross-sections and generating elements of the solid.
Calculate or simplify this relation.
$2n-3n+(n+2)=2\quad(n=12)$
This verifies the relation for this convex polyhedron family; it is not a proof for every polyhedron.

V=24, E=36, F=14; V−E+F=2.

Checks and common pitfalls: This verifies the relation for this convex polyhedron family; it is not a proof for every polyhedron.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment