DODECAHEDRON
Definition Of Dodecahedron
A Dodecahedron is a polyhedron with 12 faces.
More About Dodecahedron
A regulardodecahedron has 12 congruent faces and each face is a regular pentagon.
The surface area of a regular dodecahedron is given by the formula 
, where s is the length of each side of a pentagon.
The volume of a regular dodecahedron is given by the formula 
, where s is the length of each side of a pentagon.
Examples of Dodecahedron
There are 12 faces in this polyhedron.
All the faces are congruent and pentagonal.
So, this is a dodecahedron.
Video Examples: Sketchup, Rhombic Dodecahedron
Solved Example on Dodecahedron
Ques: Identify the net that folds into a regular dodecahedron from the following.
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. None of these
Correct Answer: A
Solution:
Step 1: Figure 1 here has 12 congruent pentagonal faces in it.
Step 2: So, it can be folded into a regular dodecahedron.
Quick Summary
- A dodecahedron is a 3D shape with 12 faces.
- A regular dodecahedron has 12 congruent regular pentagonal faces.
- Formulas exist for calculating surface area and volume based on side length.
🍎 Teacher Insights
Use physical models or interactive software to help students visualize the dodecahedron. Emphasize the importance of regular pentagons in constructing the regular dodecahedron. Relate the dodecahedron to real-world examples, such as certain dice or architectural structures.🎓 Prerequisites
- Pentagon
- Polygon
- Solid Geometry
- Area
- Volume
Check Your Knowledge
Q1: Which of the following is a dodecahedron?
Q2: What shape are the faces of a regular dodecahedron?
Frequently Asked Questions
Q: What is the difference between a dodecahedron and a regular dodecahedron?
A: A dodecahedron is any polyhedron with 12 faces. A regular dodecahedron has 12 congruent, regular pentagonal faces.
Q: How many edges and vertices does a regular dodecahedron have?
A: A regular dodecahedron has 30 edges and 20 vertices.