I have to determine the number of ways the faces of a regular tetrahedron can be colored with three colors. I already know it is 15, but apparently the math professor did not find the solution to his liking. I need to use group theory and Burnside's lemma to explain how you determine the number of ways the faces of regular tetrahedron can colored with three colors. What I understand: the basics of abstract algebra/group theory, but not much about how to apply group theory to solve this specific problem.
2026-03-27 18:09:34.1774634974
Coloring the faces of a regular tetrahedron with 3 colors using Burnside's lemma
729 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in ROTATIONS
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- why images are related by an affine transformation in following specific case?(background in computer vision required)
- Proving equations with respect to skew-symmetric matrix property
- Finding matrix linear transformation
- A property of orthogonal matrices
- Express 2D point coordinates in a rotated and translated CS
- explicit description of eigenvector of a rotation
- Finding the Euler angle/axis from a 2 axes rotation but that lies on the original 2 axes' plane
- How to find a rectangle's rotation amount that is inscribed inside an axis-aligned rectangle?
- Change of basis with rotation matrices
Related Questions in SYMMETRY
- Do projective transforms preserve circle centres?
- Decomposing an arbitrary rank tensor into components with symmetries
- A closed manifold of negative Ricci curvature has no conformal vector fields
- Show, by means of an example, that the group of symmetries of a subset X of a Euclidean space is, in general, smaller than Sym(x).
- How many solutions are there if you draw 14 Crosses in a 6x6 Grid?
- Symmetry of the tetrahedron as a subgroup of the cube
- Number of unique integer coordinate points in an $n$- dimensional hyperbolic-edged tetrahedron
- The stretch factors of $A^T A$ are the eigenvalues of $A^T A$
- The square root of a positive semidefinite matrix
- Every conformal vector field on $\mathbb{R}^n$ is homothetic?
Related Questions in COLORING
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Orbit counting lemma hexagon
- difference between colouring number and chromatic number
- Is it a tetrahedron, 5-cell, or something else?
- Distance of closest neighbor points in a vectorspace ${\mathbb R}^n$ (infinitesimal or zero)?
- How to uniquely label a connected graph?
- Graph coloring: $G$ is a graph where the number of vertices with degree of at least $k$, is at most $k$. Prove $χ(G) \le k$
- Complete graphs in the plane with colored edges where an edge don't cross edges with same color
- 4-chromatic unit distance graph with no 4-cycles.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?