Acronym  snadow, J84 
Name 
snub disphenoid, snub digonal antiprism 
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Vertex figure  [3^{4}], [3^{5}] 
Coordinates 
where r = 0.644584 is a root of r^{3}3r^{2}/2r+1=0 p = [sqrt(3/4+rr^{2})+sqrt(3/4r^{2})]/2 = 0.783931, q = [sqrt(3/4+rr^{2})sqrt(3/4r^{2})]/2 = 0.205562 
General of army  (is itself convex) 
Colonel of regiment  (is itself locally convex) 
Confer 

External links 
The provided coordinates show that snadow could be encased into a square brick A r r, where r is as given above and A=2p. Moreover the equatorial zickzack of edges and the polar digons would be completely incident to the faces of that brick.
xoBo oBox&#xt → outer heights = pq = 0.578369 inner height = 2q = 0.411123 where B = 2r = 1.289169 o... o... &  4 *  1 2 1 0  2 2 [3^{4}] .o.. .o.. &  * 4  0 2 1 2  1 4 [3^{5}] +++ x... .... &  2 0  2 * * *  2 0 digons oo.. oo..&#x &  1 1  * 8 * *  1 1 o.o. o.o.&#x &  1 1  * * 4 *  0 2 .oo. .oo.&#x  0 2  * * * 4  0 2 equatorials +++ xo.. ....&#x &  2 1  1 2 0 0  4 * ooo. ooo.&#x &  1 2  0 1 1 1  * 8
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