# 對偶多面體

## 對偶的種類

### 極點與極線互換

${\displaystyle P^{\circ }=\{q~{\big |}~q\cdot p\leq r^{2}}$ for all ${\displaystyle p}$ in ${\displaystyle P\},}$

${\displaystyle x_{0}x+y_{0}y+z_{0}z=r^{2}}$

## 參考文獻

1. Wenninger, Magnus, Dual Models, Cambridge University Press, 1983, ISBN 0-521-54325-8, MR 0730208
2. ^ Wenninger (1983)[1], "Basic notions about stellation and duality", p. 1.
3. ^ Grünbaum, Branko, Are your polyhedra the same as my polyhedra?, Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003, , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21
4. ^ Cundy, H. Martyn; Rollett, A. P., Mathematical Models 2nd, Oxford: Clarendon Press, 1961, MR 0124167
5. ^ Cundy & Rollett (1961)[4], 3.2 Duality, pp. 78–79
6. ^ Wenninger (1983)[1], Pages 3-5. (Note, Wenninger's discussion includes nonconvex polyhedra.)

t0{p,q}
{p,q}

t{p,q}
t1{p,q}
r{p,q}

2t{p,q}
t2{p,q}
2r{p,q}

rr{p,q}

tr{p,q}
ht0{p,q}
h{q,p}

s{q,p}

sr{p,q}