<prompt> Mchemraba wa kitengo una wima P_1,P_2,P_3,P_4,P_1,P_2,P_3, na P_4. Wima P_2, P_3, na P_4 ziko karibu na P_1, na kwa 1le ile 4,vituo P_i na P_i ni kinyume. Oktahedron ya kawaida ina kipeo kimoja katika kila sehemu overlineP_1P_2, overlineP_1P_3, overlineP_1P_4, overlineP_1P_2, overline P_1P_3, na jumlaP_1P_4. Pata urefu wa upande wa octahedron.asykuagiza tatu;ukubwa 5 cm;jicho mara tatu -4, -8, 3;currentprojection mtazamojicho;triple P 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1; P0 P4 kwa urahisitriple Pp -P0, -P1, -P2, -P3, -P4; chora octahedrontriple ptint k return 3Pk P14; triple ptpint k return 3Ppk Pp14; kuchorapt2--pt3--pt4--mzunguko, kijivu0.6;kuchoraptp2--pt3--ptp4--cycle, gray0.6;kuchoraptp2--pt4, kijivu0.6;kuchorapt2--ptp4, kijivu0.6;kuchorapt4--ptp3--pt2, kijivu0.6 linetype4 4;kuchoraptp4--ptp3--ptp2, kijivu0.6 linetype4 4; chora mchemrabakwaint i 0; i 4; ikuchoraP1--Pi; kuchoraPp1--Ppi;kwaint j 0; j 4; jikiwai 1 j 1 i j endelea;kuchoraPi--Ppj; kuchoraPpi--Pj;nuktaPi; nukta Ppi;nukta pti; nukta ptpi;leboP_1, P1, dirP1;leboP_2, P2, dirP2;leboP_3, P3, dir-45;leboP_4, P4, dirP4;leboP_1, Pp1, dirPp1;leboP_2, Pp2, dirPp2;leboP_3, Pp3, dir-100;leboP_4, Pp4, dirPp4;asy  <response>: Weka mchemraba katika nafasi ya kuratibu ili P_1 0,0,0 na P_1 1,1,1, na kingo za mchemraba ziwe sambamba na shoka. Kwa kuwa urefu wote wa upande wa oktahedron ni sawa, wima kwenye overlineP_1 P_2, overlineP_1 P_3, na overlineP_1 P_4 lazima ziwe sawa na P_1. Let umbali huu uwe x, hivyo kipeo kimoja kiko x,0,0. Pia, hii hufanya urefu wa upande wa octahedron x sqrt2.Vile vile, wima zingine tatu zina umbali wa x kutoka P_1, kwa hivyo moja wapo iko 1,1 - x,1.asyukubwa 7.5cm;kuagiza tatu;currentprojectionorthografia0.3,-1,0.3;nukta 34,0,0; nukta 0,0,34; nukta 0,34,0;nukta 1,1,14; nukta 1,14,1; nukta 14,1,1;chora34,0,0--0,34,0--14,1,1--1,14,1--mzunguko,nyekundu ;kuchora0,0,0--1,0,0--1,1,0--0,1,0--mzunguko;chora0,0,0--0,0,1;chora0,1,0--0,1,1;chora1,1,0--1,1,1;chora1,0,0--1,0,1;kuchora0,0,1--1,0,1--1,1,1--0,1,1--mzunguko;lebo0,0,0,0,0,0,SW,fontsize10pt;lebo1,1,1,1,1,1,NE,fontsize10pt;lebox,0,0,34,0,0,S,fontsize9pt;lebo1,0,0,1,0,0,ESE,fontsize10pt;lebo0,0,1,0,0,1,W,fontsize10pt;lebo0,1,1,0,1,1,N,fontsize10pt;lebo1,1,0,1,1,0,E,fontsize10pt;lebo0,1,0,0,1,0,NE,fontsize10pt;lebo1,1 - x,1, 1,14,1,SE,fontsize10pt;asyKwa hivyo,1 - x2 1 - x2 1 2x2.Kutatua, tunapata x frac34. Kwa hiyo, urefu wa upande wa oktahedron ni frac3 sqrt24. 