R

This discovery was by calculating with orthogonal matrices. The Clifford calculation corroborates the coincidence by appending the following to these tools.

(define mull (lambda lst (let m ((l lst))(if (null? l) C1 (C* (car l) (m (cdr l))))))) (define (d0 a)(C+ (sm (cos 0.5) C1)(sm (sin 0.5) a))) (define (d1 a)(C+ (sm (cos 0.6) C1)(sm (sin 0.6) a))) (mull (d0 (C* g2 g1)) (d1 (C* g3 g2)) (d1 (C* g1 g0)) (d0 (C* g3 g0)) (d0 (C* g1 g2)) (d1 (C* g2 g3)) (d1 (C* g0 g1)) (d0 (C* g0 g3))) ; => nearly one.This suggests, but does not prove, that there is some n(n−1)/2 (not linear) subspace of C

Even if this is so there may be other Clifford numbers in the Clifford group that are not products of unit vectors.

The C program also discovered A product that is somewhat near the identity.
Its corresponding Clifford number is `ni` below:

(define (mx fac)(if (null? fac) C1 (C* (d0 (car fac)) (mx (cdr fac))))) (define ni (mx (list (C* g0 g1)(C* g3 g1)(C* g3 g2)(C* g3 g0)(C* g2 g0) (C* g1 g0)(C* g1 g3)(C* g2 g3)(C* g3 g0)(C* g0 g2)))) ni ; => ((((0.99999798 . 0) . (0 . 0.00114777)) . ((0 . -0.00033676) . (-0.00096580 . 0))) . (((0 . -0.00095320) . (-0.00062014 . 0)) . ((-0.00062014 . 0) . (0 . -3.3447e-17))))This corresponds to the orthogonal matrix computed by the C program:

0.999997 0.001238 0.001244 0.001905 -0.001242 0.999997 0.001932 0.000670 -0.001237 -0.001932 0.999995 -0.002297 -0.001907 -0.000677 0.002294 0.999995 (Om ni) ; => ((0.99999664 0.00123843 0.00124365 0.00190538) (-0.00124211 0.99999714 0.00193161 0.00067012) (-0.00123688 -0.00193160 0.99999473 -0.00229734) (-0.00190740 -0.00067692 0.00229368 0.99999532))which is good agreement.