0
votes
1answer
48 views

How can I compute angles & lengths of the following tiling shape

a while back I created a tile made of arrows: I did it using a vector graphics software, without really understanding the properties of this shape. Now, let's say I want to write a program to ...
0
votes
0answers
13 views

For an app teaching about polyhedra, what are some core characteristics to include?

For fun: I'm building a 3d app that teaches about polyhedra. What should I include? The obvious didactic elements for each polyhedron would be: Fundamental polygon's Vertices 
Edges
 Faces
 (and ...
1
vote
2answers
47 views

Orientation of rectangle on conic section

Consider a conic section. There are 2 rectangles such that all of the 8 vertices of the 2 rectangles lie on the conic section. Further assume that the 2 rectangles have different orientation (ie. a ...
4
votes
2answers
92 views

Intersection of two tetrahedra, point reflexion

We are given a regular tetrahedron $ABCD$ ($ABC$ is its` base and $D$ is its vertex) and we reflect it through the middle of its height (point reflexion) - and thus we obtain a congruent regular ...
1
vote
1answer
24 views

Symmetries of the set of points $S$

Consider that we have a set of points $S$ in the plane $\mathbb R^2$ or in the space $\mathbb R^3$ and we also consider the one to one mappings $f:S \to S$ which have the following property: They ...
2
votes
0answers
158 views

What to call this kind of symmetry in a sphere?

Geometrically, if the two hemispheres of a spherical distribution of some kind (let's say a spherical gas cloud) are similar such that the properties of the gas as seen by a person standing on a ...
2
votes
2answers
116 views

Number of reflection symmetries of a basketball

Excerpt from John Horton Conway, The Symmetries of Things, pg. 12. Basketballs have two planes of reflective symmetry, as do tennis balls. I read this sentence and it immediately struck me as ...
1
vote
1answer
51 views

Plot the curve $y^2 = (x^2 +12x +36)/(x^4 -4x^3 - 12x^2 - 32x 64)$

Can you help me find the following to plot this curve, $$y^2 = \frac{x^2 +12x +36}{x^4 -4x^3 - 12x^2 - 32x 64}$$ In Explicit Form Find the Symmetry X & Y intercepts Vertical and Horizontal ...
1
vote
1answer
51 views

What is the value of $\angle BMN$?

here $ABC$ is a isosceles triangle.$AC=BC$,$\angle C=20$, $\angle ABM=60$ and $\angle BAN=60$.What is the value of $\angle BMN$? please help me with this problem.
1
vote
1answer
50 views

Symmetric placing of balls

Suppose I have a round domain and put my first ball in the very center (this ball alone constitutes the $0$th ring). Now around this ring (this first ball) I want to add another ring of balls in a ...
0
votes
0answers
59 views

symmetric ranges of curve division on an oloid

taken from wikipedia , I drew an Oloid by using the functions with ; ; and with ; ; If I use any equal spaced range of t(x) on ; I will end up with an unequal range t(y), which ...
0
votes
0answers
13 views

Symmetry in a $p$-sphere

Let $S(p)$ be the unit sphere at the origin in the $\mathcal{l}_p$-norm. What symmetries does it have? For instance in the $\mathcal{l}_2$-norm we have unitary symmetry in the Euclidean case. In ...
1
vote
0answers
272 views

a conjugate of a glide reflection by any isometry of the plane is again a glide reflection

Q : Prove that a conjugate of a glide reflection by any isometry of the plane is again a glide reflection, and show that the glide vectors have the same length. I know that: the conjugate ...
0
votes
2answers
259 views

Pentagon axis of symmetry

Quick question: Can a pentagon have an axis of symmetry passing through two (one, none) of its vertices? I'm given the following definition for axis of symmetry: A figure is said to have an axis of ...
8
votes
4answers
210 views

equilateral triangle; $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.$

In equilateral triangle ABC of side length d, if P is an internal point with PA = a, PB = b, and PC = c, the following pleasingly symmetrical relationship holds: $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 ...
4
votes
2answers
86 views

Automorphisms of a structure as a powerful tool for studying the structure

This is just an arbitrary testimony of an often repeated slogan: "The group of automorphisms of a given structure is often a powerful tool for studying this structure." D. Lascar, On the ...
0
votes
1answer
67 views

why are these integrals equal?

I've been trying to analyse Steiner symmetrization. I've asked before about the symmetrization preserving $\textit{volume}$, I'm still going over the same proof. I think I understand a bit what is ...
1
vote
1answer
150 views

fundamental region for the rotational symmetry group of a tetrahedron

How would I find the fundamental region of a tetrahedron for its rotational symmetry group $\mathcal{T}$? I can think of how to find these regions in 2 dimensions, but I can't wrap my mind around the ...
5
votes
1answer
182 views

Magic theorem for cylinders? Symmetry classes according to Conway's notation?

My teacher Kirsi of Mat-1.3000 in Aalto University stated 17 symmetry classes for planes and 14 for spherical things (some lecture slides here). She used Conway Thurston's notation to classify ...
0
votes
1answer
487 views

How to find the matrix of reflection operator

I got a 3D space. In got a canonical equation of a plane: $ax + by + cz+ dt = 0$ How I can find the matrix of symmetric transformation transforming a point to its reflection?
0
votes
1answer
94 views

Polyhedra with symmetries order three

If I have a natural number $o=2n$ or $4n$ I can create a polyhedron whose group of symmetries has order $o$ by making a polygon like $C_n$ and then dragging it out to make a prism (I believe this is ...