The dual of an

**isogonal**polytope is an isohedral**figure**, which is transitive on its facets. k-**isogonal**and k-uniform figures. A polytope or tiling may be called k-**isogonal**if its vertices form k transitivity classes. A more restrictive term, k-uniform is defined as an k-**isogonal figure**constructed only from regular polygons.People also ask

What is an isogonal figure?

What is dual of isogonal polytope?

What is an isogonal polyhedron?

Are there any even sided polygons that are isogonal?

That

**figure has five interior angles of 90 deg and one of 270 deg.**Those are not all equal!**Isogonal**does also imply that**the vertices are transitive,**i.e. they lie within the same symmetry orbit, something like this: o---o / \ / \ / \ o o \ / o-------oIn geometry, a

**polytope (for example,**a**polygon or a**polyhedron), or a**tiling, is isotoxal or edge-transitive if its symmetries act transitively on its**edges.Sides (2 n )468{n α } Convex β<180 Concave β>180{2 α }{3 α }{4 α }2-turn { ( n /2) α }--{ (3/2) α }2 {2 α }3-turn { ( n /3) α }----{ (4/3) α }4-turn { ( n /4) α }------Pages in category

**"Isogonal**tilings" The following 153 pages are in this category, out of 153 total. This list may not reflect recent changes ().In geometry, a

**polytope (a**polygon, polyhedron or tiling,**for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.**This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.**Isogonal figure**From**Wikipedia**the free encyclopedia In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.A facet-transitive or isotopic figure is a n -dimensional polytopes or honeycomb, with its

**facets ((n −1)- faces) congruent**and transitive. The dual of an isotope is an isogonal polytope. By definition, this isotopic property is common to the duals of the uniform polytopes. An isotopic 2-dimensional figure is isotoxal (edge-transitive).Vertex figures are especially significant for uniforms and other

**isogonal**(vertex-transitive) polytopes because one vertex**figure**can define the entire polytope. For polyhedra with regular faces, a vertex**figure**can be represented in vertex configuration notation, by listing the faces in sequence around the vertex.1948 – Herbert Wiesinger, German

**figure**skater 1949 – Thaksin Shinawatra , Thai businessman and politician, 23rd Prime Minister of Thailand 1949 – Roger Taylor , English singer-songwriter, drummer, and producer