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Iosif Pinelis
Iosif Pinelis
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For finite-dimensional $V$, your definition of a face is equivalent to the definition of a poonem, according to part (i) of Exercise 7 on page 21 of the book GruenbaumConvex Polytopes by B. Gruenbaum; then the positive answer to your question is part (iii) of Exercise 39 on the same page.

For finite-dimensional $V$, your definition of a face is equivalent to the definition of a poonem, according to part (i) of Exercise 7 on page 21 of the book Gruenbaum; then the positive answer to your question is part (iii) of Exercise 3 on the same page.

For finite-dimensional $V$, your definition of a face is equivalent to the definition of a poonem, according to part (i) of Exercise 7 on page 21 of the book Convex Polytopes by B. Gruenbaum; then the positive answer to your question is part (iii) of Exercise 9 on the same page.

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Iosif Pinelis
Iosif Pinelis
  • 127.9k
  • 8
  • 107
  • 229

For finite-dimensional $V$, your definition of a face is equivalent to the definition of a poonem, according to part (i) of Exercise 7 on page 21 of the book Gruenbaum; then the positive answer to your question is part (iii) of Exercise 3 on the same page.