Mr. A. Cay ley on Poinsot's /om/' iieiv Regular Solids. 123 



Two quantities of the compound were prepared, and submitted 

 to careful analysis, after desiccation over oil of vitriol. The fol- 

 lowing results were obtained : — 



The crystals consist therefore of iodo-arsenious acid, combined 

 with 3 equivs. of arsenious acid, AsIO^, 3AsO^. They may also 

 be regarded as a compound of teriodide of arsenic with 1 1 equivs. 

 of arsenious acid, AsP, 11 AsO^; but this constitution is not by 

 any means a probable one. 



A portion of the crystals, dried as completely as possible be- 

 tween folds of bibulous paper, lost 19 per cent, by desiccation 

 over oil of vitriol. This agrees with 12 equivs. of water, giving 

 for the composition of the crystals the formula 



AsI02,3As03 + 12H0, or AsI02,3HO + 3(As03, 3H0). 



When a large excess of hydriodic acid is present in the solu- 

 tion of iodide of arsenic in boiling water, the crystals that sepa- 

 rate on cooling consist, not of the compound described above^ 

 but of pure iodide of arsenic. It appears, therefore, that iodo- 

 arsenious acid cannot be obtained except in combination with 

 arsenious acid. 



I have endeavoured to form compounds with iodide of ammo- 

 nium and iodide of potassium, but without success. The addi- 

 tion of either of these salts to a cold saturated solution of iodide 

 of arsenic, causes the formation of pearly crystals having the 

 same composition as those obtained by cooling a hot saturated 

 solution ; while boiling-down gives rise to the separation of the 

 teriodide. 



XIX. On Poinsot's four new Regular Solids. 

 By A. Cayley, Esq.*^ 



IT is shown by Poinsot, in the " Memoire sur les Polygones et 

 les Polyedres," Jour. Puhjt. vol. iv. pp. 16 to 48 (1810), 

 that, besides the regular polyhedrons of ordinary geometry, 

 there are (of course in an extended signification of the term) 

 four new regular polyhedrons, viz. an icosahedron, which I will 

 call the great icosahedron (No. 33 of the Memoir), and tlirce 

 dodecahedrons, whicli I will call the great dodecahedron (No. 37), 

 the great stellated dodecahedron (No. 38), and the small stel- 

 lated dodecahedron (No. 39). The nature of Poiusot's genera- 



* Coniiniinicate'd Itv llic Autlior. 



