Why are all symmetry groups of regular polytopes are finite Coxeter groups?
2026-03-26 02:45:53.1774493153
Why are all symmetry groups of regular polytopes are finite Coxeter groups.
390 Views Asked by user122283 https://math.techqa.club/user/user122283/detail At
1
There are 1 best solutions below
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 POLYTOPES
- Is every finite descending sequence in [0,1] in convex hull of certain points?
- Can we really move disks around a compact surface like this?
- The permutations of (1,1,0,0), (-1,1,0,0), (-1,-1,0,0) are vertices of a polytope.
- Smoothness of a polytope
- Schlegel diagram and d-diagram
- How to find the "interior boundary" for a set of points?
- Simplicial polytope in $\mathbb{R}^n$ with $n+2$ vertices
- What are some examples of 2-polytope/3-polytope that are not simple?
- Contraction of oriented matroid as related to polytope?
- Finding the vertices of linear image of the $n$-simplex
Related Questions in COXETER-GROUPS
- Conditions for a neat subgroup to act fixed-point free
- Cardinality of a coxeter group
- The coefficient of a root in a root system must be 0 or at least 1
- In what different terms can Coxeter systems be described?
- How to obtain uniqueness in correspondence between simple systems and positive systems?
- Conjugating the longest element of a parabolic subgroup by longest element in larger parabolic?
- Two definitions of Bruhat order on $S_n$
- Combinatorics of Coxeter Groups and lenght function
- Kazhdan-Lusztig polynomials of a Dihedral group $D_n$
- What is a Coxeter Group?
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?
Because they are reflection groups, and Coxeter proved in
and in this paper in the following year that symmetries of polytopes are among the finite reflection groups:
Check out either of those two articles: Coxeter is generally easy to read.