Ltsky311,
The construction method shown in the pix you posted is a variation of the Pease panel dome method, named after the Pease Woodwork Co., of Ohio, USA. Individual triangular frames are constructed, covered in plywood or other sheathing, then bolted together. The ends of each strut of dimensional lumber (e.g., 2x3, 2x4, 2x6) making up a frame are cut at the correct compound angles to form butted joints. You glue, nail or screw the ends of the struts together to form each frame. You can also bevel-rip the struts on a table saw so that the plywood pieces sit flush on the frames. This refinement, however, isn't really necessary, especially for a dog house.
If the dog house is rehearsal for building a larger dome, then I guess it's a good way to learn the Pease method. But be forewarned: building a dome, even a small, 2-frequency hemisphere, with that construction technique is a heck of a lot of work.
An easier way to build a small dome is to cut the ends of the wooden struts at the correct axial angles. These are simple mitre cuts, not compound cuts. You then cut short sections of PVC pipe (nominal 3" pipe has an OD of 3.5") and use these as hubs to connect up all the struts. You drive screws through predrilled holes in the PVC pipe, from the inside, into the ends of the struts. Once the dome frame is complete, you can sheathe it like any other dome frame.
For a large building, the hub-screw-strut connection by itself is inadequate because tensional forces can easily pull out the screws (which are more or less aligned with the grain of the wood). But for a very small building like a dog house, this arrangement will work just fine.
Apart from not having to deal with compound angles, an advantage of the hub-&-strut method is that there are far fewer struts to deal with. In a 40-triangle panel dome, there are 120 struts (i.e., frame edges); in the hub-&-strut version, there are only 65.
Another method worth considering is that used by the Oregon Dome Inc., in the USA, for its panelized dome homes. This is similar to the Pease method, but simpler to execute, especially if you have a good table saw that can rip 2x3s through their wide face on an angle. You can also use 2x2s. Here's a link to a video by Paul Robinson in the UK. His firm, Geodome, uses this method for small, backyard greenhouse domes.
http://geo-dome.co.uk/article.asp?uname=dome_plans
For now, I'm appending some info and attaching 3 illustrations on how to build a hub-&-strut, 2-frequency hemispheric dome, 5 ft in diameter, using 2x3 lumber for the frame.
- Gerry in Québec
2v icosa hemispheric dome, class I, hub-&-strut construction
The info here is for a full dome. If you remove 5 small triangles to make a pentagonal opening, then you reduce the short-strut count by 5.
Materials/components of basic dome (excluding waterproofing)
30 short struts (A)
35 long struts (B)
6 five-way hubs with 10 holes per hub
10 six-way hubs with 12 holes per hub
5 four-way hubs (left-handed) with 8 holes per hub
5 four-way hubs (right-handed) with 8 holes per hub
10 large triangular panels (BBB)
30 small triangular panels (AAB)
260 particle board screws, 2.5" long (for connecting hubs to struts)
480 galvanized spiral nails, 2" long (for installing triangular panels over dome frame)
Struts can be cut from 2x3 lumber (1.5" x 2.5").
Triangular panels can be cut from 5/16" plywood or Oriented Strand Board (OSB)
Hubs can be cut from 3" pvc pipe (shedule 40) which has an outside diameter of 3.5".
Hubs should be predrilled, with 2 holes to accommodate each end of each strut. Total of 260 holes to drill.
Spherical radius = floor radius = 30"
Dome height = 30" + about 1" due to the 10 cylindrical hubs around the base
Vertex-to-vertex lengths (i.e., before taking into account the hub thickness)
A-type edges: chord factor 0.54653 x 30" = 16.40"
B-type edges: chord factor 0.61803 x 30" = 18.54"
Strut lengths (long edge of the strut), taking into account hub thickness:
A: 12¾"
B: 14⅞"
Mitre angle for both ends of:
A struts: 15.9º
B struts: 18º
Hub clearance:
All A struts: 9/16"
All B struts: 1/2"
Hub clearance is the distance by which a mitered strut end protrudes above the outer end of the hub. These clearances help ensure the plywood panels align properly on the dome framework.

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp+unsubscribe@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en
---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp+unsubscribe@googlegroups.com.
Am I correct in assuming that you plan on ripping the 2x4s to produce 1x4s?-Taff
--
Correction of rip specification: 0.75x3.75 ?-Taff
--


--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en
---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en
---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.