Acronym	shappy, 7/2-pyr
Name	small heptagrammic pyramid
	©
Circumradius	1/sqrt[4-1/sin2(2 π/7)] = 0.650389
Vertex figures	[37/2], [3,3,7/2]
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {7/2}:   ... between {3} and {3}:   92.09971597°
Face vector	8, 14, 8
Confer	general pyramids: n/d-py
External links

Because having axial heptagonal symmetry, the numeric values are much harder to derive algebraically. However the above given circumradius (and some further values too) get generally derived for [p,q,q]-acrohedra here by formula.

Incidence matrix according to Dynkin symbol

ox7/2oo&#x   → height = sqrt[1-1/(2 sin(2 pi/7))2] = 0.768771
(pt || {7/2})

o.7/2o.    | 1 * | 7 0 | 7 0
.o7/2.o    | * 7 | 1 2 | 2 1
-----------+-----+-----+----
oo7/2oo&#x | 1 1 | 7 * | 2 0
.x   ..    | 0 2 | * 7 | 1 1
-----------+-----+-----+----
ox   ..&#x | 1 2 | 2 1 | 7 *
.x7/2.o    | 0 7 | 0 7 | * 1