672 REPORT OF NATIONAL MUSEUM, 1897. 



Hemimorphic type. — The dihexagonal pyrauiifl. Form having the hexagonal (O) 

 axis only, with six S planes of symuietry. 



rj/ramidal-hemihedral type — The hexagonal bipyramid. Form having the hexagonal 

 (O) axis only, with ane plane, C, of symmetry. 



Tiapezohedral-hemiheclral type. — The hexagonal trapezohedron. Form having om^ 

 hexagonal (C) axis and six digoual (O) axes, with no phmo of symmetry. 



Hemimorphie-hemihedral type. — The hexagonal pyramid. Form having the hex- 

 agonal (O) axis only, with no plane of symmetry. 



Trif/onal st/stem. — Tyijes : Trigonal-hemihedral, rhombobedral-bemi- 

 hedral, heiuiniorphic-liemihedral, trigonal-tetartobedral, trape/obedral- 

 tetartobedral, rbombobedral-tetartobedral, and bemiiiiori)bic-tetarto- 

 bedral. Tbe most complete form possesses four plaues of symmetry, 

 of wbich tbree (S planes) intersect each otber at angles of 120 degrees, 

 and tbe fourtb (C) is at rigbt angles to these. 



There are four axes of symmetry, of which one, the trigonal (A) is 

 parallel to the intersections of the S planes and at right angles to the 

 C plane; tbe otber three, the digonal (O) axes, lie in the C plane at 

 right angles to tbe intersections of the S planes. 



The models illustrating the types are described as follows: 



Triyonal-hemihedral type. — The ditrigonal bipyramid. Form having the trigonal 

 (A) and three digonal (O) axes, with four planes of symmetry, one C and three S. 



Rhomhohcdral-hemihedraltype. — Thescalenohedron. Form having the trigonal (A) 

 and three digonal (O) axes, with three S planes of symmetry. 



HemlmorpliiG-liemihedral type. — The ditrigonal pyramid. Form having the trigonal 

 (A) axis, wi^h tbree S planes of symmetry. 



Trii/onal-tcfartohedral type. — Tiie trigonal bipyramid. Form having the trigonal 

 (A) axis and the plane, S, of symmetry. 



Trapezohedral-ietartohedral type. — The trigonal trapezohedron. Form having the 

 trigonal (A) and three digonal (O) axes, with no plane of symmetry. 



Uhoml)ohedral-tetartoliedral type. — The rhombohedron. Form ceutro-symmetrieal 

 and having the trigonal (A) axis. 



Heinbnorphic-tetartohedral type. — The trigonal pyramid. Form having the trigonal 

 (A) axis only, and no plane of symmetry. 



Tetragonal system. — Types : Holohedral, beraimorpbic-bemibedral, 

 pyramidal -bemibedral, trapezohedral-bemibedral, spbenoidal-bemihe- 

 dral, hemimorphic-tetartohedral, and sphenoidal-tetartobedral. The 

 most general form possesses five planes of symmetry, of wbich two 

 (S planes) are at rigbt angles to one another, and two {"2 planes) which 

 bisect tbe angles formed by tbe S planes; and another plane (C) which 

 is perpendicular to the S and 2 planes. 



There are five axes of symmetry, one of which is tetragonal ( n ) and 

 is perpendicular to the C plane and parallel to tlie intersections of two 

 S and two .5" planes, and four digonal (O) wbich lie in tbe C plane 

 and at right angles to the S and 2 planes. 



Examples of the types are described as follows : 



Uolohedrul type. — The ditetragonal bipyramid. Form having one tetragonal (D) 

 axis and four digimal (O) axes, with two S, two 2, and the C planes of symmetry. 



Jlemimorphic-hemihedral type. — The ditetragonal pyramid. Form having the tetra- 

 gonal (D) axis, with two S and two ^ planes of symmetry. 



