isogonal
isogonic

An isogonal polyhedron has a single kind of vertex figure.

It has 20 faces, each being simple concave isogonal hexagons.

We can infer the proof from existence of isogonal conjugate too.

Isogonal or vertex-transitive: all corners lie within the same symmetry orbit.

It is composed of 20 intersecting isogonal hexagon faces.

The Perpendicular bisector construction can be reversed via isogonal conjugation.

The isogonal conjugate of the incentre I is itself.

The Brocard points are isogonal conjugates of each other.

The isogonal conjugate of the circumcircle is the line at infinity.

All three of these tilings are isogonal and monohedral.

Thus, although all the vertices of a pseudo-uniform polyhedron appear the same, it is not isogonal.

The dual of an isotope is an isogonal polytope.

The isogonal conjugate of a point P is sometimes denoted by P*.

Some even-sided polygons which alternate two edge lengths, for example rectangle, are isogonal.

The isogonal conjugate of a triangle's centroid is its symmedian point.

Isogonal trajectory in curve theory.

Isogonal conjugate in triangle geometry.

All regular polygons and regular star polygons are isogonal.

(This property holds for isogonal conjugates as well.)

Because they are isogonal (vertex-transitive), their vertex arrangement uniquely corresponds to a symmetry group.

For example, the (isogonal) rectangle and (isotoxal) rhombus are duals.

The isogonal conjugate and also the complement of the orthocenter is the circumcenter.

There are an infinite number of dual uniform tilings in hyperbolic plane with isogonal irregular pentagonal faces.

Isogonal polyhedra may be classified:

A polyhedron which is isohedral and isogonal but not isotoxal is said to be noble.

This point is commonly called the first isogonic center.

Hence the 1st isogonic center is also a triangle center.

There are other center pairs besides the Fermat point and the 1st isogonic center.

In other words "'the Fermat point is coincident with the first isogonic center"'.

Lines of equal declination (isogonic lines) are shown on aeronautical and nautical charts.

This was the first such chart to be published and the first on which isogonic, or Halleyan, lines appeared.

The Fermat point has a near-identical twin called the first isogonic center or X(13) and it is important not to confuse the two.

A general isogonic chart of the world or continent can be consulted for a rough estimate of the local declination (within a few degrees)

Halley used his voyages on the pink Paramour to study the magnetic variance and was able to provide maps showing the halleyan or isogonic lines.

Information on declination for a region can be represented by a chart with isogonic lines (contour lines with each line representing a fixed declination).

Isogonic lines are where the declination has the same value, and the lines where the declination is zero are called agonic lines.

Then the lines AA', BB' and CC' are concurrent and the point of concurrence is the 1st isogonic center.

Moreover the corresponding triangle center coincides with the obtuse angled vertex whenever any vertex angle exceeds 2π/3, and with the 1st isogonic center otherwise.

The "'isogonic centers"' "X"(13) and "X"(14) are also known as the "'first Fermat point"' and the "'second Fermat point"' respectively.

In this sense, it can be said that the compass has been adjusted to indicate true north instead of magnetic north (as long as the compass remains within an area on the same isogonic line).

In the study of the Earth's magnetic field, the term isogon or isogonic line refers to a line of constant magnetic declination, the variation of magnetic north from geographic north.

Edmond Halley's General Chart of the Variation of the Compass is first published, the first to show magnetic declination (in the Atlantic Ocean) and the first on which isogonic, or Halleyan, lines appear.