Geodesic
Embeddingof a~finite $CW$-complex in a~sphere
Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 669-676.

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The following theorem is proven: for any finite $CW$-complex X of dimensionality n, no one can provide the Euclidean sphere of dimensionality $(n+1)(n+2)/2$ with a $CW$-complex structure such that $X$ will turn out to be isomorphic to some subcomplex of this $CW$-complex. 
@article{MZM_1968_4_6_a6,
     author = {Ya. N. Shapiro},
     title = {Embeddingof a~finite $CW$-complex in a~sphere},
     journal = {Matemati\v{c}eskie zametki},
     pages = {669--676},
     publisher = {mathdoc},
     volume = {4},
     number = {6},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a6/}
}
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Ya. N. Shapiro. Embeddingof a~finite $CW$-complex in a~sphere. Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 669-676. http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a6/