Intrigued by regular polyhedra for years

  • Context: High School 
  • Thread starter Thread starter DaveC426913
  • Start date Start date
  • Tags Tags
    Regular Years
Click For Summary
SUMMARY

A regular polyhedron is defined as a polyhedron where all faces are regular polygons and all polyhedral angles are congruent. When convexity is considered, only the five Platonic solids qualify as regular polyhedra. However, if concave polyhedra are included, there are four additional regular polyhedra. The discussion also clarifies that polyhedral angles refer to the angles formed by the intersection of two adjacent polygons.

PREREQUISITES
  • Understanding of polyhedra and their classifications
  • Familiarity with the concept of regular polygons
  • Knowledge of convex and concave shapes
  • Basic geometry, specifically angles and their properties
NEXT STEPS
  • Research the five Platonic solids and their properties
  • Explore the four additional regular polyhedra beyond the Platonic solids
  • Study the concept of polyhedral angles in depth
  • Investigate the mathematical implications of convexity in polyhedra
USEFUL FOR

Mathematicians, geometry enthusiasts, educators, and students interested in the properties and classifications of polyhedra.

DaveC426913
Gold Member
2025 Award
Messages
24,553
Reaction score
8,871
I've been intrigued by regular polyhedra for years, and have oft tinkered with them.

Can someone provide the "textbook definition" of a regular polyhedron?
 
Mathematics news on Phys.org
A "regular polyhedron" is a polyhedron, all of whose faces are regular polygons AND all of whose polyhedral angles are congruent.

If you add the requirement that they be convex (and was classically the case) then only the 5 "Platonic solids" are regular polyhedra. If you allow concave polyhedra, then there are 4 additional regular polyhedra.
 
Fantastic. I was specifically looking to find out whether convexity was a requirement.


Can you point me at some links that explore the additional 4 polyhedra?

Also, the "polyhedral angles" - are they merely the angle joining two adjacent polygons?
 

Similar threads

High School Tournament Permutation Problem
  • · Replies 9 ·
Replies
9
Views
2K
High School Need an on-line calculator for a simple calculation
  • · Replies 12 ·
Replies
12
Views
5K
Undergrad Distance between points on a regular tetrahedron
  • · Replies 3 ·
Replies
3
Views
3K
High School Deceptively simple geometry question on SAT test
  • · Replies 47 ·
2
Replies
47
Views
9K
Other Can't take physics my first year
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad A beginner’s thoughts on rotation number -- Resource suggestion request
  • · Replies 6 ·
Replies
6
Views
4K
Why are all NFL lineman tall?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad What is the Name of My Star Polyhedron?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad What is the point of regularization?
  • · Replies 1 ·
Replies
1
Views
2K
High School Dimensional analysis peculiarity
  • · Replies 6 ·
Replies
6
Views
2K