Copying multiple cells from multiple worksheets to one summary sheet

I am working with a workbook with over 100 sheets, so typing each line would be very time consuming.
I understand some VB coding, but not enough to write what I need myself, and therefore I do not even know if what I am asking is possible.
One of the things I would like the coding to do would be to check and get the name for each worksheet, as typing all 100+ worksheet names would be time consuming in and of itself.
I was hoping someone could help me with VB code that would accomplish what the formulas below would do in excel. There are 3 lines from each worksheet and the cells the value pull from are the same repeating patterns as indicated below for all worksheets.

Field1 Field2 Field3 Field4 Field5 Field6
=Sheet1!B3 =Sheet1!B5 =Sheet1!D20 =Sheet1!C21 =Sheet1!C22 =Sheet1!C26
=Sheet1!B3 =Sheet1!B5 =Sheet1!D29 =Sheet1!C30 =Sheet1!C31 =Sheet1!C35
=Sheet1!B3 =Sheet1!B5 =Sheet1!D38 =Sheet1!C39 =Sheet1!C40 =Sheet1!C44
=Sheet2!B3 =Sheet2!B5 =Sheet2!D20 =Sheet2!C21 =Sheet2!C22 =Sheet2!C26
=Sheet2!B3 =Sheet2!B5 =Sheet2!D29 =Sheet2!C30 =Sheet2!C31 =Sheet2!C35
=Sheet2!B3 =Sheet2!B5 =Sheet2!D38 =Sheet2!C39 =Sheet2!C40 =Sheet2!C44
=Sheet3!B3 =Sheet3!B5 =Sheet3!D20 =Sheet3!C21 =Sheet3!C22 =Sheet3!C26
=Sheet3!B3 =Sheet3!B5 =Sheet3!D29 =Sheet3!C30 =Sheet3!C31 =Sheet3!C35
=Sheet3!B3 =Sheet3!B5 =Sheet3!D38 =Sheet3!C39 =Sheet3!C40 =Sheet3!C44

Thank you in advance,

Drago

Originally Posted by oeldere

Post an excel file without confidentional information and the desired result.

example.xlsx

Attached file as requested. Obviously the actual file cannot be loaded due to privacy issues, but this shows the relevant information on sheets 2 through 4 and the desired output on sheet 1.

Thank you for taking a look at it. I'm not even certain what I'm asking is possible.