Bottle-Capped Dyson's Sphere

The dimensions of a Bottle-Capped Dyson’s Sphere are huge. It is three ships actually. First you would have an inner Dyson’s Sphere that has a diameter of 29,763 AU, then an outer Dyson’s that has a diameter of 12,759 km wider than the diameter of the inner Dyson’s Sphere. These two Dyson’s would be connected. The outer & inner Dyson’s Spheres would have a hole in them where the Bottle-Cap would fit: with a diameter of 14,878 AU. This hole would be in the north pole of the outer & inner Dyson’s Sphere. So yeah this thing would be massive. Since this would be a generational construction undertaking one would wanna build it in a different solar system than our own. That is what a Bottle-Capped Dyson’s Sphere is ok.

diameter
dimensions	AU	km	miles
inner sphere	29,763	4,452,396,782,967.9	2,767,182,587,301.4
outer sphere	29,763	4,452,396,795,726.9	2,767,182,595,231.1
bottle-cap	14,878	2,226,198,391,484.0	1,383,591,293,650.7

Warp Speeds

The Warp Speed equations are for speeds of Warp 1 to Warp 10 is V=c*W^{(3+1/3)+(-1/2*(log(10—W)))}, Warp 10 is 1600*c and Warp 11 is 1624*c; for speeds of Warp 12 and faster it's V=c*W³.
V is velocity, c is the speed of light, W is the Warp factor
In Classic Star Trek it thought that Warp 10 is possible and that you can go faster. In Star Trek TNG we learn that Warp 10 is infinite speed and you cannot go any faster. This is still in Star Trek DS9. In Star Trek Voyager we learn that Warp 10 is not infinite speed but the trans-Warp Barrier; that makes Warp 11, trans-Warp 1. This is right. In Star Trek Enterprise they do not talk about any Warp Speeds faster than Warp 5.

Warp Factor	m/s	km/h	mph	velocity*c
1	300,000,000	1,079,000,000	671,000,000	1
2	2,211,189,616	7,952,911,985	4,945,694,107	7
3	7,200,000,000	25,896,000,000	16,104,000,000	24
4	17,700,000,000	63,661,000,000	39,589,000,000	59
5	36,600,000,000	131,638,000,000	81,862,000,000	122
6	68,700,000,000	247,091,000,000	153,659,000,000	229
7	123,600,000,000	444,548,000,000	276,452,000,000	412
8	224,700,000,000	808,171,000,000	502,579,000,000	749
9	454,800,000,000	1,635,764,000,000	1,017,236,000,000	1516
10	480,000,000,000	1,726,400,000,000	1,073,600,000,000	1600	trans-Warp Barrier
11	487,200,000,000	1,752,296,000,000	1,089,704,000,000	1624	1
12	518,400,000,000	1,864,512,000,000	1,159,488,000,000	1728	2
13	659,100,000,000	2,370,563,000,000	1,474,187,000,000	2197	3
14	823,200,000,000	2,960,776,000,000	1,841,224,000,000	2744	4
15	1,012,500,000,000	3,641,625,000,000	2,264,625,000,000	3375	5
16	1,228,800,000,000	4,419,584,000,000	2,748,416,000,000	4096	6
17	1,473,900,000,000	5,301,127,000,000	3,296,623,000,000	4913	7
18	1,749,600,000,000	6,232,728,000,000	3,913,272,000,000	5832	8
19	2,057,700,000,000	7,400,861,000,000	4,602,389,000,000	6859	9
20	2,400,000,000,000	8,632,000,000,000	5,368,000,000,000	8000	10
21	2,778,300,000,000	9,992,619,000,000	6,214,131,000,000	9261	11
22	3,194,400,000,000	11,489,192,000,000	7,144,808,000,000	10648	12
23	3,650,100,000,000	13,128,193,000,000	8,164,057,000,000	12167	13
24	4,147,200,000,000	14,916,096,000,000	9,275,904,000,000	13824	14
25	4,687,500,000,000	16,859,375,000,000	10,484,375,000,000	15625	15

these Warp Speeds are just estimations.