Acronym	dap, 10-ap
Name	decagonal antiprism
Circumradius	sqrt[(3 sqrt(2)-sqrt{5+sqrt(5)})/(8 sqrt(2)-4 sqrt{5+sqrt(5)})] = 1.674505
Vertex figure	[33,10]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Confer	general antiprisms: n-ap   general polytopal classes: segmentohedra
Dihedral angles	between {3} and {3}:   arccos([1-sqrt(10+2 sqrt(5))]/3) = 159.186507° between {3} and {10}:   arccos(-sqrt[(2 sqrt(2)-sqrt(5+sqrt(5)))/(6 sqrt(2)+3 sqrt(5+sqrt(5)))]) = 95.246644°
Face vector	20, 40, 22
External links

Incidence matrix according to Dynkin symbol

s2s10s

demi( . .  .  ) | 20 |  1  1  2 | 1  3
----------------+----+----------+-----
      s2s  .    |  2 | 10  *  * | 0  2
      s .  s2*a |  2 |  * 10  * | 0  2
sefa( . s10s  ) |  2 |  *  * 20 | 1  1
----------------+----+----------+-----
      . s10s    ♦ 10 |  0  0 10 | 2  *
sefa( s2s10s  ) |  3 |  1  1  1 | * 20

s2s20o

demi( . .  . ) | 20 |  2  2 | 1  3
---------------+----+-------+-----
      s2s  .   |  2 | 20  * | 0  2
sefa( . s20o ) |  2 |  * 20 | 1  1
---------------+----+-------+-----
      . s20o   ♦ 10 |  0 10 | 2  *
sefa( s2s20o ) |  3 |  2  1 | * 20

xo10ox&#x   → height = sqrt[(sqrt(2)+sqrt(5+sqrt(5)))/(2 sqrt(2)+sqrt(5+sqrt(5)))] = 0.862397
({10} || dual {10})

o.10o.    | 10  * |  2  2  0 | 1  2  1 0
.o10.o    |  * 10 |  0  2  2 | 0  1  2 1
----------+-------+----------+----------
x.  ..    |  2  0 | 10  *  * | 1  1  0 0
oo10oo&#x |  1  1 |  * 20  * | 0  1  1 0
..  .x    |  0  2 |  *  * 10 | 0  0  1 1
----------+-------+----------+----------
x.10o.    | 10  0 | 10  0  0 | 1  *  * *
xo  ..&#x |  2  1 |  1  2  0 | * 10  * *
..  ox&#x |  1  2 |  0  2  1 | *  * 10 *
.o10.x    |  0 10 |  0  0 10 | *  *  * 1

snubbed forms: so10ox&#x