■単純リー環を使った面数数え上げ(その32)
ワイソフ算術を使って,以下の多胞体のf0,f1,fn-1も求めておきたい.
===================================
【1】正単体版
f0=n(n+1)
m=n,f1=m/2・f0=n/2・f0
{3,3}(110)→f0=12(OK)
{3,3,3}(1100)→f0=20(OK)
{3,3,3,3}(11000)→f0=30(OK)
{3,3,3,3,3}(110000)→f0=42(OK)
f1=n/2・f0
{3,3}(110)→f1=18(OK)
{3,3,3}(1100)→f1=40(OK)
{3,3,3,3}(11000)→f1=75(OK)
{3,3,3,3,3}(110000)→f1=126(OK)
fn-1=2(n+1)
{3,3}(110)→f2=8(OK)
{3,3,3}(1100)→f3=10(OK)
{3,3,3,3}(11000)→f4=12(OK)
{3,3,3,3,3}(110000)→f5=14(OK)
===================================
【2】正軸体版
f0=4n(n−1)
m=2n−3,f1=m/2・f0=(2n−3)/2・f0
{3,4}(110)→f0=24(OK)
{3,3,4}(1100)→f0=48(OK)
{3,3,3,4}(11000)→f0=80(OK)
{3,3,3,3,4}(110000)→f0=120(OK)
f1=n/2・f0
{3,4}(110)→f1=36(OK)
{3,3,4}(1100)→f1=120(OK)
{3,3,3,4}(11000)→f1=280(OK)
{3,3,3,3,4}(110000)→f1=540(OK)
fn-1=2^n+2n
{3,4}(110)→f2=14(OK)
{3,3,4}(1100)→f3=24(OK)
{3,3,3,4}(11000)→f4=42(OK)
{3,3,3,3,4}(110000)→f5=76(OK)
===================================