Elements of mineralogy, crystallography and blowpipe analysis from a practical standpoint .. . Fig. 26 shows the form a:\a:ia for which the diedral anglesA, B, C, Fig. 27, are A= 158° 13; B= 149°, C= 158° 13; Fig. 27 shows « : 2a : 4« for which A = 162° 15; ^ = 154° A7, C= 144° 3- That the symmetry of the group requires forty-eight such faces to satisfy it mayreadily be proved by Fig. 28 which is simply an eighth (or octant) of Fig. 24 enlarged,0 being the center, OA, OB and OC the crystal axes and OX an axis of trigonal sym-metry. If any face I, with intercepts on OA, OB, OC respectively, l :
Elements of mineralogy, crystallography and blowpipe analysis from a practical standpoint .. . Fig. 26 shows the form a:\a:ia for which the diedral anglesA, B, C, Fig. 27, are A= 158° 13; B= 149°, C= 158° 13; Fig. 27 shows « : 2a : 4« for which A = 162° 15; ^ = 154° A7, C= 144° 3- That the symmetry of the group requires forty-eight such faces to satisfy it mayreadily be proved by Fig. 28 which is simply an eighth (or octant) of Fig. 24 enlarged,0 being the center, OA, OB and OC the crystal axes and OX an axis of trigonal sym-metry. If any face I, with intercepts on OA, OB, OC respectively, l : 3 : | occurs, itmust be accompanied by faces 2 and 3 because OX is an axis of trigonal symmetry, andthe three white planes of symmetry make necessary planes 4, 5 and 6. Finally theentire octant must be reflected in each of the other octants by the shaded planes ofsymmetry. The Limit Forms. The general form for special positions of the faces passes intolimit forms. Six suppositions may be made each of which corre- H CR YSTALLO GRAPH Y. spends to a limit-form. Denoting infinity by o
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