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The augmented hexagonal prism is Johnson solid J_(54), which is formed from augmentation of one of the lateral faces of an equilateral hexagonal prism by an equilateral ...

The augmented pentagonal prism is Johnson solid J_(52), which is formed from augmentation of one of the lateral faces of an equilateral pentagonal prism by an equilateral ...

The augmented sphenocorona is Johnson solid J_(87), which is formed from augmentation of one of the square faces of the sphenocorona by an equilateral square pyramid. The ...

The augmented triangular prism is Johnson solid J_(49), which is formed from augmentation of one of the lateral faces of an equilateral triangular prism by an equilateral ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

There are two different definitions of the mid-arc points. The mid-arc points M_(AB), M_(AC), and M_(BC) of a triangle DeltaABC as defined by Johnson (1929) are the points on ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...